Even Numbers: Definition, Properties, List, Examples, Facts

What Are Even Numbers?

Even numbers are the numbers that are evenly divisible by 2. When divided by 2, even numbers leave a remainder of 0. Even numbers always end with 0, 2, 4, 6, or 8.

Even numbers can be easily divided into equal groups. How? Let’s see! Can you count the number of kids and tell me if you can divide them equally among 2 teams? 

There are 4 kids. They can be easily divided into two equal teams since 4 is an even number. 

Even Numbers: Definition

Even numbers are numbers divisible by “2.” The numbers that have the digits “0,” “2,” “4,” “6,” or “8” in the ones place are even numbers.

Even numbers examples: 22, 56, 98,  2, -16, 452, -867454, 12, 5752452, -98534, etc.

How to Identify Even Numbers

To identify even numbers, we observe the last digit or the ones digit of the number. If it ends in the digits 0, 2, 4, 6, or 8, then it is an even number. Otherwise, it is an odd number.

Example 1: 248

Hundreds	Tens	Ones
2	4	8
Even Number

Example 2: 103

Hundreds	Tens	Ones
1	0	3
Odd Number

Another way is to divide the number by 2. If the remainder is “0,” then it is an even number; if the remainder is 1, then it is an odd number.   

Example 1: $\frac{72}{2} = 36$ and remainder $= 0$

Thus, 72 is an even number.

Example 2:  $\frac{35}{2} = 17$ R 1 since $(17 \times 2) + 1 = 35$

Thus, 35 is an odd number.

Even Numbers on a Number Line

On a number line, if you start from 0 and keep taking jumps of 2, you will land on 2, 4, 6, 8, 10, and so on. These are even numbers.

If you make the jumps of 2 to the left of 0, you will meet the negative integers that are even. Notice that between two even numbers, there’s an odd number!

General Form of an Even Number

Let n be any integer, then even numbers can be expressed as 2n.

General form of even numbers $= 2$n n is an integer

For example, if $n = 3$, we get an even number 6.

For $n = \;-\;5$, we get an even number $\;-\;10$.

List of Even Numbers up to 100

Even Numbers up to 100
2	4	6	8	10
12	14	16	18	20
22	24	26	28	30
32	34	36	38	40
42	44	46	48	50
52	54	56	58	60
62	64	66	68	70
72	74	76	78	80
82	84	86	88	90

Properties of Even Numbers

1. Property of Addition:

• Even number $+$ Odd number $=$ Odd number.

For example, $8 + 5 = 13$.

• Even number $+$ Even number $=$ Even number.

For example, $8 + 4 = 12$.

• Odd number $+$ Odd number $=$ Even number.

For example, $3 + 5 = 8$.

2. Property of Subtraction:

• Even number $-$ Odd number $=$ Odd number

For example, $8 \;-\; 5 = 3$.

• Even number $-$ Even number $=$ Even number

For example, $16 \;-\; 10 = 6$.

• Odd number $-$ Odd number $=$ Even number

For example, $13 \;-\; 5 = 8$.

We can summarize the addition and subtraction properties as follows:

Addition	Subtraction	Result
Even $+$ Even	Even $-$ Even	Even
Even $+$ Odd	Even $-$ Odd	Odd
Odd $+$ Even	Odd $-$ Even	Odd
Odd $+$ Odd	Odd $-$ Odd	Even

3. Property of Multiplication:

• Multiplying an even number and an odd number (and vice versa) always results in an even number.

For example, $5 \times 6 = 30$.

• Multiplying an even number with an even number always results in an even number.

For example, $6 \times 10 = 60$.

• Multiplying odd and odd always results in an odd number.

For example, $13 \times 5 = 65$.

Operation$(\times)$	Result
Even $\times$ Even	Even
Even $\times$ Odd	Even
Odd $\times$ Even	Even
Odd $\times$ Odd	Odd

Facts about Even Numbers

Conclusion

In this article, we learned about even numbers, their properties, how to identify even numbers and the list of even numbers. Let’s solve a few examples and practice problems to understand this better. 

Solved Examples on Even Numbers

1. Identify the even numbers from the given list.

$23, \;8,\; 46,\; 81,\; \;-\; 96,\; 73,\; \;-\;11,\; 62,\; 33,\; 74$

Solution:

Even numbers are divisible by 2 and end in the digits “0”,”2″, “4”, “6” or “8”.  

The even numbers here are $8 ,\; 46,\;\;-\;96,\;  62,\; 74$.                               

2. Find the sum of even numbers between 50 and 60.

Solution: 

The even numbers that lie between 50 and 60 are as follows: 

$52,\; 54,\; 56,\; 58$

$52 + 54 + 56 + 58 = 220$

Sum $= 220$

3. Check whether the number of objects in the image are even or odd.

Solution: 

There are 11 apples. 

11 apples cannot be divided into two equal groups. If we divide 11 by 2, the remainder is 1. One apple will be left over. 

Thus, 11 is an odd number.

4.  What is the sum of the smallest and the largest three-digit even numbers?

Solution: 

The smallest three-digit even number $= 100$

The largest three-digit even number  $= 998$

Sum of the numbers $= 100+ 998= 1098$

5.  The lengths of the sides of a triangle are consecutive even numbers. Find out what the length of the longest side is if the perimeter of the triangle is 24 units?

Solution: 

Let n be any positive number. Three consecutive even numbers can be represented as 

$2n,\; 2n + 2,\; 2n + 4$

So, $2n,\; 2n + 2,$ &  $2n + 4$ be the lengths of the triangle.

Perimeter of triangle $=$ Sum of all the sides

$\Rightarrow 24 = 2n + 2n + 2 + 2n + 4$

$\Rightarrow 24 = 6n + 6$

$\Rightarrow 6n = 18$

$\Rightarrow n = 18 \div 6$

$\Rightarrow n = 3$

Hence, the lengths of the sides are

$2n = 2 \times 3 = 6$

$2n + 2 = 2 \times 3 + 2 = 8$

$2n + 4 = 2 \times 3 + 4 = 10$

So, the length of the longest side is 10 units.

Practice Problems on Even Numbers

Frequently Asked Questions about Even Numbers