# What is an even number ?  Definition and examples.

An even number is an integer that can be grouped in twos. For example, it is possible to group 4 computers in groups of twos only. Therefore, 4 is an even number. As you can see from the illustration above, an even number is never going to have a remainder of 1 when you try to make groups of twos.

In the example above, there are two groups of two computers.

In other words, 4 = 2 × 2

6 will give you 3 groups of 2 and we can write it as

6 =  2 × 3

8 is also an even number and we can write it as 8 =  2 × 4

A negative integer can also be an even number as long as you can show that there is no remainder of 1.

For example,  -4 = 2 × -2 and  -6 = 2 × -3

Do you see a pattern? The numbers in red do not change. The other number in black is an integer.

Formal definition of  even number :

Let n be an integer, then 2n is an even number.

By definition, 0 is an even number since 0 times anything is 0 and therefore will never leave a remainder of 1.. The definition of even numbers apply only to integers! It would not make sense to say that a fraction, a decimal, or a real number is an even number.