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What Is an Even Number? (Mathematics Glossary)

What Is an Even Number?

An even number is a whole number that can be divided exactly by 2.

Dictionary Definition

The Oxford English Dictionary defines an even number as a number "divisible integrally into two equal parts; opposed to odd."

Examples of Even Numbers

Some examples of even numbers are given below:

Even Numbers on a Number Line

The image below shows the even numbers on the number line.

How to Check if a Number Is an Even Number

A number is even if it can be divided exactly by 2.

An Example Question

Is 24 an even number?
Step 1
Divide the number by 2.
24 ÷ 2 = 12
Step 2
Check if the answer from Step 1 is a whole number. If it is, the original number is even. Else it is odd.

In our example, 12 is a whole number.

24 is an even number.

A Formula to Generate Even Numbers

The formula below generates even numbers:



If k takes a whole number (1, 2, 3...), then n will always be even.
k = 0 ∴ n = 2k = 2 × 0 = 0
k = 1 ∴ n = 2k = 2 × 1 = 2
k = 2 ∴ n = 2k = 2 × 2 = 4
k = 3 ∴ n = 2k = 2 × 3 = 6
k = 4 ∴ n = 2k = 2 × 4 = 8

A Real Example of Even Numbers

The slider below shows a real example of even numbers:
Interactive Test
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Here's a second test on even numbers.
Here's a third test on even numbers.
Here's a dynamic test on even numbers.
Top Tip

A Quick Way to See If a Number Is Even

A number is even if its last digit is 0, 2, 4, 6 or 8.

Note

Odd Numbers

If a number isn't even, it is odd.

An odd number is a whole number that cannot be divided exactly by 2.

A number is odd if its last digit is 1, 3, 5, 7 or 9.

The formula below generates odd numbers:



If k takes a whole number (1, 2, 3...), then n will always be odd.