## Divisibility by 5 and 10

This is the third post in the Divisibility Rules Series. The first was about divisibility by 2 and the second was about divisibility by 4. In this post, we discuss divisibility by 5 and 10.

If we skip count by 10, we will immediately realize that the numbers always end in zero: 10, 20, 30, 40, and so on. It is clear that all multiples of 10 end in 0; therefore, a number is divisible by 10 if the ones digit is 0.

On the other hand, if we skip count by 5, then we have 5, 10, 15, 20, 25, 30 and so on. Notice that if we add 5 to a number whose ones digit is 5, the ones digit of the sum is 0. Similarly, any number whose ones digit is 0 added to 5, the ones digit of the sum is always 5. Hence, we conclude that a number is divisible by 5, if the ones digit is either 5 or 0.

From here, we can see clearly that all numbers that are divisible by 10 are also divisible by 5.