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.