{"id":41935,"date":"2024-05-30T06:57:02","date_gmt":"2024-05-30T06:57:02","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=41935"},"modified":"2024-05-30T07:07:58","modified_gmt":"2024-05-30T07:07:58","slug":"factor-tree-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree","title":{"rendered":"Factor Tree \u2013 Definition with 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-2564c605-3cf7-4845-8cf0-64fe2335a1a0\" 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\/factor-tree#0-what-is-a-factor-tree>What Is a Factor Tree?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree#2-what-is-splitting-numbers-and-branching>What Is Splitting Numbers and Branching?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree#3-how-to-draw-a-factor-tree-of-a-number>How to Draw a Factor Tree of a Number<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree#8-solved-examples-on-factor-trees>Solved Examples on Factor Trees<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree#9-practice-problems-on-factor-trees>Practice Problems on Factor Trees<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree#10-frequently-asked-questions-about-factor-trees>Frequently Asked Questions about Factor Trees<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-a-factor-tree\">What Is a Factor Tree?<\/h2>\n\n\n\n<p><strong>A factor tree is a diagram that breaks down a composite number into its prime factors. It starts with the given number at the top and branches out, with each branch representing a factor of the previous number. This process continues until all the branches reach prime numbers. The last numbers (leaf nodes) represent the prime factorization of the original number.&nbsp;<\/strong><\/p>\n\n\n\n<p>The general method to find the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/prime-factorization\">prime factorization<\/a> can be tedious for large numbers. Factor tree provides a quick, simple, and systematic way to understand the prime factorization of numbers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"566\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-supporting-image.png\" alt=\"Factor tree - supporting image\" class=\"wp-image-41942\" title=\"Factor tree - supporting image\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-supporting-image.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-supporting-image-300x274.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>What Are Factors?<\/strong><\/p>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/factor\">factor<\/a> is a number that divides a given number evenly without leaving a remainder.&nbsp;<\/p>\n\n\n\n<p>When we multiply two numbers to find the product, both the numbers being multiplied are called factors of the product.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>1 \u00d7 15 = 15<\/p>\n\n\n\n<p>3 \u00d7 5 = 15\u00a0<\/p>\n\n\n\n<p>So, 15 has four factors: 1, 3, 5, and 15.&nbsp;<\/p>\n\n\n\n<p>However, this method can be inconvenient for larger numbers. That&#8217;s where the factor tree method comes in.<\/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\/complete-factor-pairs-for-a-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\/algebra_complete_factor_pair_pt.png\" alt=\"Complete Factor Pairs for a 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\">Complete Factor Pairs for a 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\/fill-in-the-missing-factors\" 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\/algebra_missing_factor_pt.png\" alt=\"Fill in the Missing Factors 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\">Fill in the Missing Factors 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-factor-tree-definition\">Factor Tree: Definition<\/h2>\n\n\n\n<p>A factor tree is a visual representation or a diagram that breaks down a given number into its prime factors. It is a prime factorization method, which expresses a composite number as a product of prime numbers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"618\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-150.png\" alt=\"Factor tree of 150\" class=\"wp-image-41943\" title=\"Factor tree of 150\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-150.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-150-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-150-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-150-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-150-120x120.png 120w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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\/factors-of-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\/factors-of-10.jpeg\" alt=\"Factors of 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\/factors-of-12\" 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\/factors-of-12.jpeg\" alt=\"Factors of 12\">\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\/factors-of-14\" 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\/factors-of-14.jpeg\" alt=\"Factors of 14\">\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\/factors-of-15\" 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\/factors-of-15.jpeg\" alt=\"Factors of 15\">\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\/factors-of-16\" 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\/factors-of-16.jpeg\" alt=\"Factors of 16\">\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\/factors-of-18\" 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\/factors-of-18.jpeg\" alt=\"Factors of 18\">\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\/factors-of-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\/factors-of-20.jpeg\" alt=\"Factors of 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\/factors-of-21\" 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\/factors-of-21.jpeg\" alt=\"Factors of 21\">\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\/factors-of-22\" 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\/factors-of-22.jpeg\" alt=\"Factors of 22\">\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\/factors-of-24\" 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\/factors-of-24.jpeg\" alt=\"Factors of 24\">\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-is-splitting-numbers-and-branching\">What Is Splitting Numbers and Branching?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Splitting Numbers in a Factor Tree:<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Splitting numbers in a factor tree refers to breaking down a composite number into its factors.<\/p>\n\n\n\n<p>When you start with a composite number as the root of the factor tree, you split it into two or more factors along branches.<\/p>\n\n\n\n<p>These factors can be prime or composite, and the process continues until you reach prime factors at the end of the branches.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"446\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/splitting-numbers-in-a-factor-tree-example.png\" alt=\"Splitting numbers in a factor tree - example\" class=\"wp-image-41944\" title=\"Splitting numbers in a factor tree - example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/splitting-numbers-in-a-factor-tree-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/splitting-numbers-in-a-factor-tree-example-300x216.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Branching in a Factor Tree:<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Branching in a factor tree involves extending lines or branches from a number to represent its factors or divisors. Each branch represents one of the factors of the number from which it originates. The branching process continues until all factors are expressed as prime numbers, creating a visual representation of the prime factorization of the original composite number.<\/p>\n\n\n\n<p>In summary, splitting numbers involves breaking down a composite number into its factors, while branching represents the visual connections between these factors in a factor tree, ultimately leading to the prime factorization of the original number.<\/p>\n\n\n\n<p><strong>Example: <\/strong>We can express 120 as the product of 12 and 10.&nbsp;<\/p>\n\n\n\n<p>120 = 12 \u00d7 10\u00a0<\/p>\n\n\n\n<p>Both 12 and 10 are, again, composite numbers.&nbsp;<\/p>\n\n\n\n<p>12 = 4 \u00d7 3<\/p>\n\n\n\n<p>10 = 2 \u00d7 5<\/p>\n\n\n\n<p>Next, we can write 4 as<\/p>\n\n\n\n<p>4 = 2 \u00d7 2<\/p>\n\n\n\n<p>Now, we have reached the end since we obtained all the prime factors, 2, 3, 4, and 5.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-draw-a-factor-tree-of-a-number\">How to Draw a Factor Tree of a Number<\/h2>\n\n\n\n<p><strong>Step 1: <\/strong>Write the composite number at the top of the tree. (This number is often termed as the root number of the factor tree.)<\/p>\n\n\n\n<p><strong>Step 2: <\/strong>Identify two numbers that multiply together to give the root number. These factors can be prime or composite.&nbsp;<\/p>\n\n\n\n<p><strong>Step 3<\/strong>: Determine if the factor is prime or composite for each branch.<\/p>\n\n\n\n<p>If it&#8217;s composite, continue branching until you reach prime factors.<\/p>\n\n\n\n<p><strong>Step 4: <\/strong>Continue this process for each composite factor, branching out and factoring until you have expressed all factors as primes.&nbsp;<\/p>\n\n\n\n<p><strong>Step 5: <\/strong>The factor tree is complete when there are prime numbers at the end of each branch.<\/p>\n\n\n\n<p><strong><em>Note:<\/em><\/strong><em> To create a systematic pattern, encircle the prime factors and draw a box around the composite factors.<\/em><\/p>\n\n\n\n<p><strong>Factor Tree Examples:<\/strong><\/p>\n\n\n\n<p><strong>Example 1:<\/strong> Factor tree of 120<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"617\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-120.png\" alt=\"Factor tree of 120\" class=\"wp-image-41945\" title=\"Factor tree of 120\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-120.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-120-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-120-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-120-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-120-120x120.png 120w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Example 2:<\/strong> Factor tree of 12<\/p>\n\n\n\n<p>Find the factor tree of 12.<\/p>\n\n\n\n<p>12 = 2 \u00d7 6<\/p>\n\n\n\n<p>2 is prime. 6 is composite.<\/p>\n\n\n\n<p>12 = 2 \u00d7 (2 \u00d7 3)<\/p>\n\n\n\n<p>Thus, 12 = 2 \u00d7 2 \u00d7 3<\/p>\n\n\n\n<p>12 = 2<sup>2<\/sup> \u00d7 3<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"524\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-12.png\" alt=\"Factor tree of 12\" class=\"wp-image-41946\" title=\"Factor tree of 12\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-12.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-12-300x254.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Example 3<\/strong>: Factor tree of 60<\/p>\n\n\n\n<p>60 = 2 \u00d7 30<\/p>\n\n\n\n<p>60 = 2 \u00d7 3 \u00d7 5 \u00d7 2<\/p>\n\n\n\n<p>60 = 2 \u00d7 2 \u00d7 3 \u00d7 5<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"533\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-60.png\" alt=\"Factor tree of 60\" class=\"wp-image-41947\" title=\"Factor tree of 60\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-60.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-60-300x258.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-prime-factor-tree\">Prime Factor Tree<\/h2>\n\n\n\n<p>A prime factor tree specifically aims to find the prime factorization of a composite number. The focus is solely on breaking down the number into its prime components.&nbsp;<\/p>\n\n\n\n<p>The primary purpose of a prime factor tree is to express a composite number as a product of its prime factors, simplifying it to its prime form.<\/p>\n\n\n\n<p>A <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/prime-number\">prime number<\/a> is a natural number with only two factors: 1 and the number itself.&nbsp;<\/p>\n\n\n\n<p>Examples: 2, 3, 5, 7,&#8230;<\/p>\n\n\n\n<p><strong>Example 1: <\/strong>Find the prime factorization of 72<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"615\" height=\"663\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/prime-factorization-of-72.png\" alt=\"Prime factorization of 72\" class=\"wp-image-41948\" title=\"Prime factorization of 72\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/prime-factorization-of-72.png 615w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/prime-factorization-of-72-278x300.png 278w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><\/figure>\n\n\n\n<p><strong>Example 2:<\/strong> <strong>Factor tree of 180<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"642\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-180.png\" alt=\"Factor tree of 180\" class=\"wp-image-41949\" title=\"Factor tree of 180\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-180.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-180-290x300.png 290w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>NOTE:<\/strong> A number can have multiple factor trees, which ultimately give the same prime factorization. The prime factorization is unique, but a factor tree can have different forms depending on how you break down the number.<\/p>\n\n\n\n<p>Here are two different factor trees of 64:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"445\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-trees-of-64.png\" alt=\"Factor trees of 64\" class=\"wp-image-41950\" title=\"Factor trees of 64\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-trees-of-64.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-trees-of-64-300x215.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Prime factorization of 64 = 2<sup>6<\/sup><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-applications-of-a-factor-tree\">Applications of a Factor Tree<\/h2>\n\n\n\n<p>1) To find the prime factors of a number<\/p>\n\n\n\n<p>2) To write the prime factorization of a number<\/p>\n\n\n\n<p>3) To find the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd\">GCD (Greatest Common Divisor)<\/a> of a number<\/p>\n\n\n\n<p>4) to find the LCM (Least Common Multiple) of a number<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-facts-about-factor-trees\">Facts about Factor Trees<\/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 endpoints of the tree represent prime factors, as they cannot be further factored. They are also called \u201cleaf nodes.&#8221;<\/li>\n\n\n\n<li>The prime factorization of any number is always unique. However, the factor<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about Factor Trees, a method for finding a number&#8217;s prime factors. We discussed how to draw a factor tree, its applications, and associated concepts. Let\u2019s solve a few examples for better comprehension and reinforcement.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-solved-examples-on-factor-trees\">Solved Examples on Factor Trees<\/h2>\n\n\n\n<p><strong>1. Draw a factor tree for 24.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>24 = 2 \u00d7<\/strong> <strong>1<\/strong><strong>2<\/strong><\/p>\n\n\n\n<p><strong>24 = 2 \u00d7<\/strong> <strong>2 \u00d7<\/strong> <strong>6<\/strong><\/p>\n\n\n\n<p><strong>24 = 2<\/strong> \u00d7<strong>2 \u00d7 2 \u00d7<\/strong> <strong>3<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"288\" height=\"255\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-24.png\" alt=\"Factor tree of 24\" class=\"wp-image-41951\" title=\"Factor tree of 24\"\/><\/figure>\n\n\n\n<p><strong>2. Write the prime factorization of 36 using a factor tree.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Here\u2019s the factor tree and prime factorization of 36:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"281\" height=\"344\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-36.png\" alt=\"Factor tree of 36\" class=\"wp-image-41952\" title=\"Factor tree of 36\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-36.png 281w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-36-245x300.png 245w\" sizes=\"auto, (max-width: 281px) 100vw, 281px\" \/><\/figure>\n\n\n\n<p><strong>3. Draw a factor tree for 80.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p>Factor tree of 80:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"325\" height=\"308\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-80.png\" alt=\"Factor tree of 80\" class=\"wp-image-41953\" title=\"Factor tree of 80\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-80.png 325w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-80-300x284.png 300w\" sizes=\"auto, (max-width: 325px) 100vw, 325px\" \/><\/figure>\n\n\n\n<p><strong>4. Write the prime factors of 156 using the factor tree method.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Here\u2019s a factor tree of 156:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"379\" height=\"191\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-156.png\" alt=\"Factor tree of 156\" class=\"wp-image-41954\" title=\"Factor tree of 156\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-156.png 379w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-156-300x151.png 300w\" sizes=\"auto, (max-width: 379px) 100vw, 379px\" \/><\/figure>\n\n\n\n<p>Prime factors of 156: 2, 3, and 13<\/p>\n\n\n\n<p><strong>5. Draw a factor tree of 84.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Factor tree of 84:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"267\" height=\"242\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-84.png\" alt=\"Factor tree of 84\" class=\"wp-image-41955\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-practice-problems-on-factor-trees\">Practice Problems on Factor Trees<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Factor Tree \u2013 Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Find the missing number in the factor tree of 125.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/finding-the-missing-number-in-the-factor-tree-of-125.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">15<\/div><div class=\"spq_answer_block\" data-value=\"1\">25<\/div><div class=\"spq_answer_block\" data-value=\"2\">5<\/div><div class=\"spq_answer_block\" data-value=\"3\">120<\/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: 25<br\/>There are two ways to find the missing numbers.<br>\r\nDivide 125 by 5.<br>\r\n$125 \\div 5 = 25$<br>\r\nOR multiply two numbers forming the two branches.<br>\r\n$5 \\times 5 = 25$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">A prime number has ___ factors.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">3<\/div><div class=\"spq_answer_block\" data-value=\"2\">5<\/div><div class=\"spq_answer_block\" data-value=\"3\">0<\/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: 2<br\/>A prime number has only two factors.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following prime factorizations are correct?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$36 = 2 \\times 2 \\times 3 \\times 5$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$75 = 3 \\times 5 \\times 6$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$125 = 5 \\times 5 \\times 7$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$108 = 2 \\times 2 \\times 3 \\times 3 \\times 3$<\/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: $108 = 2 \\times 2 \\times 3 \\times 3 \\times 3$<br\/>Prime factorization of $108 = 2 \\times 2 \\times 3 \\times 3 \\times 3$<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-108.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Write the prime factorization of 92 using the given factor tree.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-92.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$92 = 2 \\times 4 \\times 23$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$92 = 2 \\times 2 \\times 46$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$92 = 2 \\times 2 \\times 23$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$92 = 2 \\times 2 \\times 46 \\times 23$<\/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: $92 = 2 \\times 2 \\times 23$<br\/>$92 = 2 \\times 2 \\times 23$<\/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\": \"Factor Tree \u2013 Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Factor Tree\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the missing number in the factor tree of 125.\",\n                    \"text\": \"Find the missing number in the factor tree of 125. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/finding-the-missing-number-in-the-factor-tree-of-125.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"There are two ways to find the missing numbers.<br>\r\nDivide 125 by 5.<br>\r\n$$125 \\\\div 5 = 25$$<br>\r\nOR multiply two numbers forming the two branches.<br>\r\n$$5 \\\\times 5 = 25$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are two ways to find the missing numbers.<br>\r\nDivide 125 by 5.<br>\r\n$$125 \\\\div 5 = 25$$<br>\r\nOR multiply two numbers forming the two branches.<br>\r\n$$5 \\\\times 5 = 25$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are two ways to find the missing numbers.<br>\r\nDivide 125 by 5.<br>\r\n$$125 \\\\div 5 = 25$$<br>\r\nOR multiply two numbers forming the two branches.<br>\r\n$$5 \\\\times 5 = 25$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"120\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"There are two ways to find the missing numbers.<br>\r\nDivide 125 by 5.<br>\r\n$$125 \\\\div 5 = 25$$<br>\r\nOR multiply two numbers forming the two branches.<br>\r\n$$5 \\\\times 5 = 25$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"25\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"There are two ways to find the missing numbers.<br>\r\nDivide 125 by 5.<br>\r\n$$125 \\\\div 5 = 25$$<br>\r\nOR multiply two numbers forming the two branches.<br>\r\n$$5 \\\\times 5 = 25$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"There are two ways to find the missing numbers.<br>\r\nDivide 125 by 5.<br>\r\n$$125 \\\\div 5 = 25$$<br>\r\nOR multiply two numbers forming the two branches.<br>\r\n$$5 \\\\times 5 = 25$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A prime number has ___ factors.\",\n                    \"text\": \"A prime number has ___ factors.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A prime number has only two factors.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A prime number has only two factors.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A prime number has only two factors.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A prime number has only two factors.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"2\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A prime number has only two factors.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A prime number has only two factors.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following prime factorizations are correct?\",\n                    \"text\": \"Which of the following prime factorizations are correct?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Prime factorization of $$108 = 2 \\\\times 2 \\\\times 3 \\\\times 3 \\\\times 3$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$36 = 2 \\\\times 2 \\\\times 3 \\\\times 5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Prime factorization of $$108 = 2 \\\\times 2 \\\\times 3 \\\\times 3 \\\\times 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$75 = 3 \\\\times 5 \\\\times 6$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Prime factorization of $$108 = 2 \\\\times 2 \\\\times 3 \\\\times 3 \\\\times 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$125 = 5 \\\\times 5 \\\\times 7$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Prime factorization of $$108 = 2 \\\\times 2 \\\\times 3 \\\\times 3 \\\\times 3$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$108 = 2 \\\\times 2 \\\\times 3 \\\\times 3 \\\\times 3$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Prime factorization of $$108 = 2 \\\\times 2 \\\\times 3 \\\\times 3 \\\\times 3$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-108.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Prime factorization of $$108 = 2 \\\\times 2 \\\\times 3 \\\\times 3 \\\\times 3$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-108.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Write the prime factorization of 92 using the given factor tree.\",\n                    \"text\": \"Write the prime factorization of 92 using the given factor tree. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/factor-tree-of-92.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$92 = 2 \\\\times 2 \\\\times 23$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$92 = 2 \\\\times 4 \\\\times 23$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$92 = 2 \\\\times 2 \\\\times 23$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$92 = 2 \\\\times 2 \\\\times 46$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$92 = 2 \\\\times 2 \\\\times 23$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$92 = 2 \\\\times 2 \\\\times 46 \\\\times 23$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$92 = 2 \\\\times 2 \\\\times 23$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$92 = 2 \\\\times 2 \\\\times 23$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$92 = 2 \\\\times 2 \\\\times 23$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$92 = 2 \\\\times 2 \\\\times 23$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-frequently-asked-questions-about-factor-trees\">Frequently Asked Questions about Factor Trees<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-1fe15c44-49d9-4b57-a490-f6b30c384c40\" 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-0-1fe15c44-49d9-4b57-a490-f6b30c384c40\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1fe15c44-49d9-4b57-a490-f6b30c384c40\"><strong>What are factor trees?<\/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-0-1fe15c44-49d9-4b57-a490-f6b30c384c40\">\n\n<p>Factor trees are a visual way to show how numbers can be broken down into their prime factors (numbers divisible only by 1 and themselves).<\/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-1-1fe15c44-49d9-4b57-a490-f6b30c384c40\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1fe15c44-49d9-4b57-a490-f6b30c384c40\"><strong>How do I make a factor tree?<\/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-1-1fe15c44-49d9-4b57-a490-f6b30c384c40\">\n\n<ul class=\"wp-block-list\">\n<li>Start with your number at the top. Find two factors that multiply to make that number. Write them below, branching out like a tree.<\/li>\n\n\n\n<li>Repeat for each factor, breaking them down further until you reach prime numbers.<\/li>\n<\/ul>\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-2-1fe15c44-49d9-4b57-a490-f6b30c384c40\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1fe15c44-49d9-4b57-a490-f6b30c384c40\"><strong>What are 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-2-1fe15c44-49d9-4b57-a490-f6b30c384c40\">\n\n<p>Prime numbers are only divisible by 1 and themselves (e.g., 2, 3, 5, 7, 11).<\/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-3-1fe15c44-49d9-4b57-a490-f6b30c384c40\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-1fe15c44-49d9-4b57-a490-f6b30c384c40\"><strong>What are some uses of factor trees?<\/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-3-1fe15c44-49d9-4b57-a490-f6b30c384c40\">\n\n<ul class=\"wp-block-list\">\n<li>Finding prime factors of a number.<\/li>\n\n\n\n<li>Checking if a number is prime.<\/li>\n\n\n\n<li>Finding the least common multiple (LCM) or greatest common factor (GCF) of two numbers (more advanced).<\/li>\n<\/ul>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Factor Tree? A factor tree is a diagram that breaks down a composite number into its prime factors. It starts with the given number at the top and branches out, with each branch representing a factor of the previous number. This process continues until all the branches reach prime numbers. The last &#8230; <a title=\"Factor Tree \u2013 Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/factor-tree\" aria-label=\"More on Factor Tree \u2013 Definition with 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":[],"tags":[],"class_list":["post-41935","post","type-post","status-publish","format-standard","hentry"],"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\/41935","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=41935"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/41935\/revisions"}],"predecessor-version":[{"id":41963,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/41935\/revisions\/41963"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=41935"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=41935"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=41935"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}