Divisibility by 2

Integers exactly divisible by 2 are called even; integers not divisible by 2 are called odd.

In the set of natural numbers, for example, numbers 2, 4, 6, 8,.......1000 are even and
numbers 1, 3, 5, 7, 9,......1001 are odd.

0 is considered an even number.

10 is exactly divisible by 2. Every number ending with zero can be represented as a sum of tens.
For example: 30 = 10 + 10 + 10; 50 = 10 + 10 + 10 + 10 + 10

Therefore, because each 10 in the sum is exactly divisible by 2, we can make a conclusion that 

every number ending in 0 is divisible by 2.

For example: Numbers 90, 150, 700 are divisible by 2, because they end in 0.

A multi-digit number that does not end in 0 can be presented as a sum of a number ending in 0 and a one-digit number. For example, 596 = 590 + 6

The first addend, 590, is divisible by 2, because it ends in 0. The second addend, 6, is also divisible by 2, hense the number 596 is divisible by 2.

Let us consider 597. We represent it as 590 + 7. Again, the first addend is divisible by 2, but the second one is 7 and it is not divisible by 2. If exactly one of the addends is not divisible by 2, then the sum is not divisible by 2, therefore 597 is not divisible by 2.

So, 596 is divisible by 2 because its last digit is an even number, and 597 is not divisible by 2 because its last digit is an odd number.

Therefore, an integer is even if its last digit represents an even number.

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