# 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

24 ÷ 2 = 12

Step 2

**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

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

**show**

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.