{"id":31465,"date":"2023-07-05T07:37:58","date_gmt":"2023-07-05T07:37:58","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31465"},"modified":"2023-07-05T09:28:24","modified_gmt":"2023-07-05T09:28:24","slug":"greatest-common-divisor-gcd-definition-methods-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd","title":{"rendered":"Greatest Common Divisor (GCD): Definition, Methods,\u00a0 Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-d2d79b16-05ef-4df2-b558-1cab2f1a3931\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd#0-what-is-the-greatest-common-divisor-gcd>What Is the Greatest Common Divisor (GCD)?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd#4-how-to-find-the-gcd-greatest-common-divisor>How to Find the GCD (Greatest Common Divisor)<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd#11-greatest-common-divisor-formula>Greatest Common Divisor Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd#16-solved-examples-on-the-greatest-common-divisor>Solved Examples on the Greatest Common Divisor<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd#17-practice-problems-on-the-greatest-common-divisor>Practice Problems on the Greatest Common Divisor<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd#18-frequently-asked-questions-about-greatest-common-divisor>Frequently Asked Questions about Greatest Common Divisor<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-greatest-common-divisor-gcd\">What Is the Greatest Common Divisor (GCD)?<\/h2>\n\n\n\n<p><strong>The greatest common divisor (GCD), also known as \u201cgreatest common factor (GCF)\u201d or \u201chighest common factor (HCF)\u201d, of two numbers is the greatest factor that divides both the numbers. In simple words, it is the largest factor shared between two or more numbers.&nbsp;<\/strong><\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/arrange-the-decimal-numbers-from-smallest-to-greatest\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_order_dec_2_pt.png\" alt=\"Arrange the Decimal Numbers From Smallest to Greatest Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Arrange the Decimal Numbers From Smallest to Greatest Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-greatest-or-least-decimal\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/decimals_make_way_24_gm.png\" alt=\"Choose Greatest or Least Decimal Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose Greatest or Least Decimal Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-greatest-or-least-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_make_way_13_gm.png\" alt=\"Choose Greatest or Least Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose Greatest or Least Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-divisor\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_miss_num_div_c_pt.png\" alt=\"Choose the Correct Divisor Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Correct Divisor Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/compare-to-find-least-or-greatest-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_greatest_least_2_pt.png\" alt=\"Compare to Find Least or Greatest Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Compare to Find Least or Greatest Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-division-equation-by-filling-the-quotient-or-divisor\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_pv_miss_num_div_d_pt.png\" alt=\"Complete the Division Equation by FIlling the Quotient or Divisor Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Division Equation by FIlling the Quotient or Divisor Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-greatest-or-least-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_make_way_15_gm.png\" alt=\"Find Greatest or Least Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Greatest or Least Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/find-least-or-greatest-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/count_comp_greatest_least_1_pt.png\" alt=\"Find Least or Greatest Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Find Least or Greatest Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-common-attributes-in-different-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_common_attribute_pt.png\" alt=\"Identify Common Attributes in Different Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Common Attributes in Different Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/identify-common-attributes-in-shapes\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geometry_shared_attribute_pt.png\" alt=\"Identify Common Attributes in Shapes Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Identify Common Attributes in Shapes Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-definition-of-greatest-common-divisor\">Definition of Greatest Common Divisor<\/h2>\n\n\n\n<p>The greatest common divisor (GCD) of two integers can be defined as the largest positive integer that is a divisor of both numbers. It is also called the highest common factor (HCF) or the greatest common factor (GCF).&nbsp;<\/p>\n\n\n\n<p>The GCD of two numbers a and b is sometimes written as GCD(a, b) or gcd(a, b).<\/p>\n\n\n\n<p>For example, the GCD of 8 and 12 is 4.&nbsp;<\/p>\n\n\n\n<p>GCD$(8, 12) = 4$<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/choose-the-greatest-number-within-1000\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/choose-the-greatest-number-within-1000.jpeg\" alt=\"Choose the Greatest Number within 1000\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-and-find-the-greatest-number-within-10\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-and-find-the-greatest-number-within-10.jpeg\" alt=\"Compare and Find the Greatest Number within 10\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-and-find-the-greatest-number-within-20\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-and-find-the-greatest-number-within-20.jpeg\" alt=\"Compare and Find the Greatest Number within 20\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-fractions-by-finding-common-denominator\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-fractions-by-finding-common-denominator.jpeg\" alt=\"Compare Fractions by Finding Common Denominator Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/comparing-and-finding-the-greatest-number-within-100\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/comparing-and-finding-the-greatest-number-within-100.jpeg\" alt=\"Comparing and Finding the Greatest Number within 100\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-common-denominator-compare-unlike-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/find-common-denominator-compare-unlike-fractions.jpeg\" alt=\"Find Common Denominator & Compare Unlike Fractions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-the-greatest-and-the-smallest-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/find-the-greatest-and-the-smallest-numbers.jpeg\" alt=\"Find the Greatest and the Smallest Numbers\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/find-the-greatest-decimal\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/find-the-greatest-decimal.jpeg\" alt=\"Find the Greatest Decimal\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/form-smallest-and-greatest-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/form-smallest-and-greatest-numbers.jpeg\" alt=\"Form Smallest and Greatest Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/form-the-greatest-and-the-smallest-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/form-the-greatest-and-the-smallest-number.jpeg\" alt=\"Form the Greatest and the Smallest Number Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-what-are-factors\">What Are Factors?<\/h2>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/factor\">factor<\/a> of a number is a number that divides the given number evenly without leaving a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/remainder\">remainder<\/a>. Factors are numbers that you can multiply together to get another number, called the product. Every number has at least two factors.<\/p>\n\n\n\n<p><strong>Example 1: <\/strong>$2 \\times 4 = 8$.<\/p>\n\n\n\n<p>So, 2 and 4 are both factors of 8.<\/p>\n\n\n\n<p><strong>Example 2: <\/strong>We can write 12 as&nbsp;<\/p>\n\n\n\n<p>$12 = 1 \\times 12$<\/p>\n\n\n\n<p>$12 = 2 \\times 6$<\/p>\n\n\n\n<p>$12 = 3 \\times 4$<\/p>\n\n\n\n<p>Therefore 1, 2, 3, 4, 6, and 12 are all factors of 12.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-what-are-common-factors\">What Are Common Factors?<\/h2>\n\n\n\n<p>As the name implies, a common factor is a factor common between two or more numbers. In other words, it is a number that can evenly divide a set of two or more numbers.<\/p>\n\n\n\n<p>We can find the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/common-factor\">common factors<\/a> of two or more numbers by listing the factors of each number and then identify the factors that are common among them.&nbsp;<\/p>\n\n\n\n<p><strong>Example 1: Find the common factors of 15 and 20.<\/strong><\/p>\n\n\n\n<p>Factors of $15 = 1, 3, 5, 15$<\/p>\n\n\n\n<p>Factors of $20 = 1, 2, 4, 5, 10, 20$<\/p>\n\n\n\n<p>Factors common in 15 and 20 are 1 and 5.<\/p>\n\n\n\n<p><strong>Example 2: Find common factors of 16 and 24.<\/strong><\/p>\n\n\n\n<p>Factors of $16 = 1, 2, 4, 8, 16$<\/p>\n\n\n\n<p>Factors of $24 = 1, 2, 3, 4, 6, 8, 12, 24$<\/p>\n\n\n\n<p>Common factors of 16 and $24 = 1, 2, 4, 8$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"429\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/common-factors.png\" alt=\"Common factors of 16 and 24 visual\" class=\"wp-image-31471\" title=\"Common factors of 16 and 24 visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/common-factors.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/common-factors-300x208.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-how-to-find-the-gcd-greatest-common-divisor\">How to Find the GCD (Greatest Common Divisor)<\/h2>\n\n\n\n<p>In order to determine the greatest common divisor for a pair of two positive integers (m, n), follow the steps listed below:<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Write the factors of the positive integer &#8220;m.&#8221;<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Write the factors of the positive integer &#8220;n.&#8221;<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Identify the common divisors of &#8220;m&#8221; and &#8220;n.&#8221;<\/p>\n\n\n\n<p><strong>Step 4:<\/strong> Find the divisor that is the largest among the common divisors of &#8220;m&#8221; and &#8220;n.&#8221;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-methods-to-find-the-greatest-common-divisor\">Methods to Find the Greatest Common Divisor<\/h2>\n\n\n\n<p>There are numerous ways to determine the biggest common divisor of two numbers. The methods to find G.C.D. are as follows.<\/p>\n\n\n\n<p>1. Listing method<\/p>\n\n\n\n<p>2. Prime factorization method<\/p>\n\n\n\n<p>3. Long division method<\/p>\n\n\n\n<p>4. Repeated division method<\/p>\n\n\n\n<p>5. Euclid\u2019s division algorithm<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-gcd-by-listing-method\">GCD by Listing Method<\/h2>\n\n\n\n<p>In this method, we list the factors of the given numbers and then highlight the common factors. After identifying the common factors, we find the largest common factor.<\/p>\n\n\n\n<p><strong>Example: Find the GCD of 24 and 30 using the listing method.<\/strong><\/p>\n\n\n\n<p>Factors of $24 =\u00a0 1, 2, 3, 4, 6, 8, 12, 24$<\/p>\n\n\n\n<p>Factors of $30 = 1, 2, 3, 5, 6, 10, 15, 30$<\/p>\n\n\n\n<p>Common factors of 24 and $30 = 1, 2, 3, 6$<\/p>\n\n\n\n<p>G.C.D. of 24 and $30 = 6$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-gcd-by-prime-factorisation-method\">GCD by Prime Factorisation Method<\/h2>\n\n\n\n<p>In this method, we find the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/prime-factorization\">prime factorization<\/a> of the given numbers using the factor tree method or division method. Using the prime factorization, find the common factors between the two numbers. Multiply these together to find the greatest common divisor. This method is applicable only for positive integers.<\/p>\n\n\n\n<p><strong>Example 1: Find the greatest common divisor of 24 and 30.<\/strong><\/p>\n\n\n\n<p>Let\u2019s find the prime factorization of 24 and 30 using the factor tree method.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"517\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/prime-factorization.png\" alt=\"Prime factorization of 24 and 36\" class=\"wp-image-31472\" title=\"Prime factorization of 24 and 36\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/prime-factorization.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/prime-factorization-300x250.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Prime factors of $24 = 2 \\times 2 \\times 3$<\/p>\n\n\n\n<p>Prime factors of $36 = 2 \\times 2 \\times 3 \\times 3$<\/p>\n\n\n\n<p>Common factors of 24 and $36 = 2, 2, 3$<\/p>\n\n\n\n<p>G.C.D. of 24 and $36 =\u00a0 2 \\times 2 \\times 3 = 12$<\/p>\n\n\n\n<p><strong>Example 2:<\/strong> <strong>&nbsp;Find the greatest common factor of 168 and 180.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Prime factors of $160 = 2^{3} \\times 3 \\times 7 = 2 \\times 2 \\times 2 \\times 3 \\times 7$<\/p>\n\n\n\n<p>Prime factors of $180 = 2^{2}\\times 3^{2} \\times 5 = 2 \\times 2\\times 3 \\times 3 \\times 5$<\/p>\n\n\n\n<p>The common factors are $2 \\times 2 \\times 3 = 12$<\/p>\n\n\n\n<p>Therefore, greatest common factor of $(168, 180) = 12$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-gcd-by-long-division-method\">GCD by Long Division Method<\/h2>\n\n\n\n<p>The long division method is more useful for finding GCD of large numbers. The steps to be followed for long division method are as follows:&nbsp;<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Divide the large number by the smaller one.&nbsp;<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Treat the remainder obtained as the new divisor and set the previous divisor as the new dividend.<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Divide the first divisor by the first remainder.<\/p>\n\n\n\n<p><strong>Step 4:<\/strong> Divide the second divisor by the second remainder.<\/p>\n\n\n\n<p><strong>Step 5: <\/strong>Continue this process till the remainder becomes 0.<\/p>\n\n\n\n<p><strong>Step 6: <\/strong>The divisor, which does not leave a remainder, is the G.C.D. of the two numbers and thus, the last divisor is the required G.C.D. of the given numbers.<\/p>\n\n\n\n<p><strong>Example 1: Find GCD of 105 and 189 using the long division method.&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"661\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-using-division.png\" alt=\"Finding GCD of 189 and 105 long division method\" class=\"wp-image-31473\" title=\"Finding GCD of 189 and 105 long division method\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-using-division.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-using-division-281x300.png 281w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Since the last divisor that we got is 21, we can say that the greatest common divisor of 105 and 189 is 21.<\/p>\n\n\n\n<p>G.C.D. of 105 and $189 = 21$.<\/p>\n\n\n\n<p><strong>Example 2: Find GCD of 32, 56, and 46.<\/strong><\/p>\n\n\n\n<p>To find the GCD of three numbers, we start by using the long division on any two numbers. Once the division is complete, we divide the remaining number by the last divisor obtained in the first division.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"459\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-of-three-numbers.png\" alt=\"GCD of 32, 56, and 46 using long division method.\" class=\"wp-image-31475\" title=\"GCD of 32, 56, and 46 using long division method.\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-of-three-numbers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-of-three-numbers-300x222.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-gcd-by-repeated-division-method\">GCD by Repeated Division Method<\/h2>\n\n\n\n<p>This method is pretty similar to the long division method. Let\u2019s understand the steps.<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Divide the given numbers by the smallest common prime factor.<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Divide the quotients thus obtained by their smallest common prime factor.<\/p>\n\n\n\n<p><strong>Step 3:<\/strong> Repeat until there is no more common prime factor between the quotients.&nbsp;<\/p>\n\n\n\n<p><strong>Step 4:<\/strong> Multiply all the divisors (prime factors).<\/p>\n\n\n\n<p><strong>Example: Find the G.C.D. of 24 and 36 using repeated division.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"516\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-repeated-division-example.png\" alt=\"GCD of 24 and 36 using repeated division\" class=\"wp-image-31476\" title=\"GCD of 24 and 36 using repeated division\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-repeated-division-example.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-repeated-division-example-300x249.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-gcd-by-euclid%E2%80%99s-division-algorithm\">GCD by Euclid\u2019s Division Algorithm<\/h2>\n\n\n\n<p>This method is applicable only for positive integers. Euclid\u2019s division algorithm is based on the Euclid\u2019s division lemma. It is a method used to find GCD of two positive integers.<\/p>\n\n\n\n<p>According to Euclid&#8217;s division lemma, if we have two positive integers a and b, then there would be whole numbers q and r that satisfy the equation $a = bq + r$, where $0 \\le r \\lt b$.\u00a0<\/p>\n\n\n\n<p>Using this lemma, we express the larger number \u201ca\u201d in terms of the smaller number \u201cb\u201d in the quotient remainder form $a = b q + r$.\u00a0<\/p>\n\n\n\n<p>If $r = 0$, then b is the G.C.D. of a and b.\u00a0<\/p>\n\n\n\n<p>If r 0, then we again use the lemma on the numbers b and r as GCD (b, r) $=$ GCD (a, b).<\/p>\n\n\n\n<p>Repeat the above process until the remainder is zero. When the remainder is zero, the last divisor is the GCD of given numbers. (OR the last non-zero remainder is the GCD.)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If $a = 0$, then GCD $(a, b) = b$<\/li>\n<\/ul>\n\n\n\n<p>GCD $(0, b) = b$.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If $b = 0$, then GCD $(a, b) = a$<\/li>\n<\/ul>\n\n\n\n<p>GCD $(a, 0) = a$.<\/p>\n\n\n\n<p><strong>Example 1: Find the G.C.D. of 123 and 36.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"474\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-euclids-algorithm.png\" alt=\"Euclid\u2019s division algorithm\" class=\"wp-image-31477\" title=\"Euclid\u2019s division algorithm\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-euclids-algorithm.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-euclids-algorithm-300x229.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Example 2: Find the G.C.D. of 1180 and 482.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"504\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-euclids-algorithm-example.png\" alt=\"GCD of 123 and 36 using Euclid\u2019s algorithm\" class=\"wp-image-31478\" title=\"GCD of 123 and 36 using Euclid\u2019s algorithm\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-euclids-algorithm-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/gcd-using-euclids-algorithm-example-300x244.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Thus, gcd$(1180, 482) = 2$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-greatest-common-divisor-formula\">Greatest Common Divisor Formula<\/h2>\n\n\n\n<p>If a and b are positive integers, then the greatest common divisor of a and b can be given by:<\/p>\n\n\n\n<p><strong>\u00a0GCD <\/strong>$(a,b) = \\frac{a \\times b}{LCM (a, b)}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-finding-greatest-common-divisor-by-lcm-method\">Finding Greatest Common Divisor by LCM Method<\/h2>\n\n\n\n<p>The greatest common factor can be found using the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple\">LCM<\/a> method using the following formula:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"384\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/Greatest-Common-Divisor-7.png\" alt=\"LCM method formula\" class=\"wp-image-31479\" title=\"LCM method formula\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/Greatest-Common-Divisor-7.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/Greatest-Common-Divisor-7-300x186.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The steps to calculate the GCD of (a, b) using the LCM method is:<\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Find the product of a and b.<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Find the least common multiple (LCM) of a and b.<\/p>\n\n\n\n<p><strong>Step 3: <\/strong>Divide the product by LCM.<\/p>\n\n\n\n<p><strong>Step 4: <\/strong>The obtained value is the greatest common divisor of (a, b).<\/p>\n\n\n\n<p><strong>Example: If the LCM(24, 36) = 72, find the GCD(24, 36).<\/strong><\/p>\n\n\n\n<p>GCD $(a, b) = \\frac{a \\times b}{LCM (a, b)}$<\/p>\n\n\n\n<p>GCD $(24, 36) = \\frac{24 \\times 36}{LCM (24, 36)}= \\frac{24 \\times 36}{72} = 12$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-applications-of-greatest-common-divisor\">Applications of Greatest Common Divisor<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>To simplify <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/fraction\">fractions<\/a> or ratios, to reduce them to their simplest form.<\/li>\n<\/ol>\n\n\n\n<p>Example: To find the simplest form of $\\frac{35}{50}$, we find the gcd(35, 50).\u00a0\u00a0<\/p>\n\n\n\n<p>GCD$(35,50) = 5$<\/p>\n\n\n\n<p>Divide both the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/numerator\">numerator<\/a> and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/denominator\">denominator<\/a> by the gcd.<\/p>\n\n\n\n<p>$\\frac{35 \\div 5}{50 \\div 5} = \\frac{7}{10}$<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>To find the LCM of the given numbers.<\/li>\n<\/ol>\n\n\n\n<p>LCM $(a, b) = \\frac{a \\times b}{GCD(a, b)}$<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li>The concept of GCD is used in many real-life situations, such as dividing a group of people into smaller sections, arranging students in rows and columns of equal numbers.<br><\/li>\n\n\n\n<li>GCD has interesting applications in geometry as well. For example, we can determine the side of the largest square tile that can cover the rectangular floor of dimensions \u201ca b\u201d by finding the GCD(a,b).<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-facts-about-greatest-common-divisor\">Facts about Greatest Common Divisor<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The GCD (Greatest Common Divisor) is also known as HCF (Highest Common Factor) or GCF (Greatest Common Factor).<\/li>\n\n\n\n<li>The formal definition of GCD is credited to Euclid who discussed it in his book \u201celements.\u201d<\/li>\n\n\n\n<li>Two numbers are said to be relatively prime if their greatest common factor (GCD) is 1.<\/li>\n\n\n\n<li>When one number is a multiple of the other, the smaller number is the GCD and the greater number is the LCM.<\/li>\n\n\n\n<li>The GCD of two <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/prime-number\">prime numbers<\/a> is always 1.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"15-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we have learned about the greatest common divisors and methods of finding them. Let us solve some greatest common divisor examples using those methods.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"16-solved-examples-on-the-greatest-common-divisor\">Solved Examples on the Greatest Common Divisor<\/h2>\n\n\n\n<p><strong>1. Find GCD of 16 and 60 using the long division method.&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"301\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-example.png\" alt=\"Finding GCD of 16 and 60 using long division method\" class=\"wp-image-31480\" title=\"Finding GCD of 16 and 60 using long division method\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-example.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-example-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-example-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-gcd-example-120x120.png 120w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<p>Since last divisor is 4, GCD of 16 and 60 = 4<\/p>\n\n\n\n<p><strong>2. Find the greatest common factor of 150 and 180 by using the prime factorization method.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Prime factors of $150 = 2 \\times 3 \\times 5^{2} = 2 \\times 3 \\times 5 \\times 5$<\/p>\n\n\n\n<p>Prime factors of $180 = 2^{2}\\times 3^{2}\\times 5 = 2 \\times 2 \\times 3 \\times 3 \\times 5$<\/p>\n\n\n\n<p>The common factors $= 2, 3, 5$<\/p>\n\n\n\n<p>GCD $(150, 180) = 2 \\times 3 \\times 5 = 30$<\/p>\n\n\n\n<p>Therefore, greatest common factor of $(150, 180) = 30$<\/p>\n\n\n\n<p><strong>3. If the LCM of 15 and 70 is 210, find the greatest common divisor of 15 and 70.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>$a = 15 , b = 70$<\/p>\n\n\n\n<p>The greatest common divisor of 15 and 70 can be calculated using the given formula:<\/p>\n\n\n\n<p>GCD $(a,b) = \\frac{a \\times b}{LCM (a, b)}$<\/p>\n\n\n\n<p>Thus, GCD $(a,b) = \\frac{15 \\times 70}{210} =\u00a0 5$<\/p>\n\n\n\n<p>Therefore, the greatest common divisor of (15, 70) is 5.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"17-practice-problems-on-the-greatest-common-divisor\">Practice Problems on the Greatest Common Divisor<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Greatest Common Divisor (GCD): Definition, Methods,\u00a0 Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Greatest common divisor (GCD) is also known as<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Greatest Common Factor<\/div><div class=\"spq_answer_block\" data-value=\"1\">Highest Common Divisor<\/div><div class=\"spq_answer_block\" data-value=\"2\">Greatest Common Measure<\/div><div class=\"spq_answer_block\" data-value=\"3\">All of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: All of the above<br\/>GCM (Greatest Common Measure), GCF (Greatest Common Factor), HCF (Highest Common Factor) are other names for GCD.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the GCD of 8 and 12?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8<\/div><div class=\"spq_answer_block\" data-value=\"1\">12<\/div><div class=\"spq_answer_block\" data-value=\"2\">2<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 4<br\/>GCD is the largest positive integer that divides each of the integers.<br>\r\nFactors of $8 = 1, 2, 4, 8$<br>\r\nFactors of $12 = 1, 2, 3, 4, 6, 12$<br>\r\nCommon factors $= 1, 2, 4$<br>\r\nSo, the GCD of 8 and 12 is 4.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">GCD$(5, 7) =$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">5<\/div><div class=\"spq_answer_block\" data-value=\"3\">7<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>5 and 7 are relatively prime numbers. The only common factor between them is 1.<br>\r\nGCD$(5, 7) = 1$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Greatest Common Divisor (GCD): Definition, Methods,\u00a0 Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Greatest Common Divisor (GCD)\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    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Measure), GCF (Greatest Common Factor), HCF (Highest Common Factor) are other names for GCD.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Highest Common Divisor\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"GCM (Greatest Common Measure), GCF (Greatest Common Factor), HCF (Highest Common Factor) are other names for GCD.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Greatest Common Measure\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"GCM (Greatest Common Measure), GCF (Greatest Common Factor), HCF (Highest Common Factor) are other names for GCD.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"All of the above\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"GCM (Greatest Common Measure), GCF (Greatest Common Factor), HCF (Highest Common Factor) are other names for GCD.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"GCM (Greatest Common Measure), GCF (Greatest Common Factor), HCF (Highest Common Factor) are other names for GCD.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the GCD of 8 and 12?\",\n                    \"text\": \"What is the GCD of 8 and 12?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"GCD is the largest positive integer that divides each of the integers.<br>\r\nFactors of $$8 = 1, 2, 4, 8$$<br>\r\nFactors of $$12 = 1, 2, 3, 4, 6, 12$$<br>\r\nCommon factors $$= 1, 2, 4$$<br>\r\nSo, the GCD of 8 and 12 is 4.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"GCD is the largest positive integer that divides each of the integers.<br>\r\nFactors of $$8 = 1, 2, 4, 8$$<br>\r\nFactors of $$12 = 1, 2, 3, 4, 6, 12$$<br>\r\nCommon factors $$= 1, 2, 4$$<br>\r\nSo, the GCD of 8 and 12 is 4.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"GCD is the largest positive integer that divides each of the integers.<br>\r\nFactors of $$8 = 1, 2, 4, 8$$<br>\r\nFactors of $$12 = 1, 2, 3, 4, 6, 12$$<br>\r\nCommon factors $$= 1, 2, 4$$<br>\r\nSo, the GCD of 8 and 12 is 4.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"GCD is the largest positive integer that divides each of the integers.<br>\r\nFactors of $$8 = 1, 2, 4, 8$$<br>\r\nFactors of $$12 = 1, 2, 3, 4, 6, 12$$<br>\r\nCommon factors $$= 1, 2, 4$$<br>\r\nSo, the GCD of 8 and 12 is 4.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"4\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"GCD is the largest positive integer that divides each of the integers.<br>\r\nFactors of $$8 = 1, 2, 4, 8$$<br>\r\nFactors of $$12 = 1, 2, 3, 4, 6, 12$$<br>\r\nCommon factors $$= 1, 2, 4$$<br>\r\nSo, the GCD of 8 and 12 is 4.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"GCD is the largest positive integer that divides each of the integers.<br>\r\nFactors of $$8 = 1, 2, 4, 8$$<br>\r\nFactors of $$12 = 1, 2, 3, 4, 6, 12$$<br>\r\nCommon factors $$= 1, 2, 4$$<br>\r\nSo, the GCD of 8 and 12 is 4.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"GCD$$(5, 7) =$$\",\n                    \"text\": \"GCD$$(5, 7) =$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"5 and 7 are relatively prime numbers. The only common factor between them is 1.<br>\r\nGCD$$(5, 7) = 1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 and 7 are relatively prime numbers. The only common factor between them is 1.<br>\r\nGCD$$(5, 7) = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 and 7 are relatively prime numbers. The only common factor between them is 1.<br>\r\nGCD$$(5, 7) = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"7\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 and 7 are relatively prime numbers. The only common factor between them is 1.<br>\r\nGCD$$(5, 7) = 1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"5 and 7 are relatively prime numbers. The only common factor between them is 1.<br>\r\nGCD$$(5, 7) = 1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"5 and 7 are relatively prime numbers. The only common factor between them is 1.<br>\r\nGCD$$(5, 7) = 1$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"18-frequently-asked-questions-about-greatest-common-divisor\">Frequently Asked Questions about Greatest Common Divisor<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-3a71c58f-18e3-4a65-a109-d47bde99d302\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-3a71c58f-18e3-4a65-a109-d47bde99d302\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3a71c58f-18e3-4a65-a109-d47bde99d302\"><strong>What are co-prime numbers ?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-3a71c58f-18e3-4a65-a109-d47bde99d302\">\n\n<p>Co-prime numbers, also known as relative prime or mutually prime numbers, are numbers that have no common factor other than 1. A set of co-prime numbers must consist of at least two numbers. Co-prime numbers have only one common factor between them. For example, 4 (an even square number) and 7 (prime number) are co-prime.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-3a71c58f-18e3-4a65-a109-d47bde99d302\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3a71c58f-18e3-4a65-a109-d47bde99d302\"><strong>What is LCM?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-3a71c58f-18e3-4a65-a109-d47bde99d302\">\n\n<p>LCM is the short form for \u201cLeast Common Multiple.\u201d It is defined as the smallest multiple that two or more numbers have in common.<\/p>\n\n\n\n<p>Consider two integers, 2 and 3.&nbsp;<\/p>\n\n\n\n<p>Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20\u2026<\/p>\n\n\n\n<p>Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 \u2026<\/p>\n\n\n\n<p>6, 12, 18, \u2026 are common multiples of 2 and 3. The number 6 is the smallest. Therefore, 6 is the least common multiple of 2 and 3.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-3a71c58f-18e3-4a65-a109-d47bde99d302\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3a71c58f-18e3-4a65-a109-d47bde99d302\"><strong>What is the difference between GCD and LCM?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-3a71c58f-18e3-4a65-a109-d47bde99d302\">\n\n<p>GCD, or Greatest Common Divisor, is the largest number that will divide all the other numbers of the group without leaving a remainder. So, it is smaller than all the numbers or, at the most, is equal to the smallest number of the group.<\/p>\n\n\n\n<p>LCM or Lowest Common multiple is the smallest number that is a multiple of all the other numbers of the group. So, it is larger than all the numbers or, at the most, is equal to the largest number of the group.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-3a71c58f-18e3-4a65-a109-d47bde99d302\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3a71c58f-18e3-4a65-a109-d47bde99d302\"><strong>What is the difference between multiples and factors?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-3a71c58f-18e3-4a65-a109-d47bde99d302\">\n\n<p>A multiple is a product that we get when the given number is multiplied by an integer. For example: 12 is a multiple of 3 because $3 \\times 4 = 12$<\/p>\n\n\n\n<p>A factor is a number that divides a given number completely without leaving a remainder.For example: 3 and 4 are factors of 12 because $3 \\times 4 = 12$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-3a71c58f-18e3-4a65-a109-d47bde99d302\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-3a71c58f-18e3-4a65-a109-d47bde99d302\"><strong>What is the meaning of GCD? Are GCD and HCF the same?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-3a71c58f-18e3-4a65-a109-d47bde99d302\">\n\n<p>GCD stands for the greatest common divisor. It is the largest positive integer that divides both the given numbers. HCF stands for highest common factor. HCF and GCD mean the same thing.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Greatest Common Divisor (GCD)? The greatest common divisor (GCD), also known as \u201cgreatest common factor (GCF)\u201d or \u201chighest common factor (HCF)\u201d, of two numbers is the greatest factor that divides both the numbers. In simple words, it is the largest factor shared between two or more numbers.&nbsp; Recommended Games Arrange the Decimal &#8230; <a title=\"Greatest Common Divisor (GCD): Definition, Methods,\u00a0 Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd\" aria-label=\"More on Greatest Common Divisor (GCD): Definition, Methods,\u00a0 Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-31465","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31465","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=31465"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31465\/revisions"}],"predecessor-version":[{"id":31489,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31465\/revisions\/31489"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31465"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31465"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31465"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}