The Proof of Divisibility By 5

This is the fourth post in the divisibility series for middle school students. In this post, I am going to discuss divisibility by 5. This is probably one of the easiest divisibility rules to remember and to prove. I am sure you are all familiar that a number ends in 0 or 5, then it is divisible by 5. Therefore, we have two cases.

Theorem

If a number ends in 0 or 5, then it is divisible by 5.

Proof

Numbers Ending in 0

All numbers ending in 0 can be expressed as 10n where n is some numbers. For example, 30 can be expressed as 10(3) and 120 can be expressed as 10(12). Now, since 10 is divisible by 5, so 10n is divisible by 5. This means that all numbers ending in 0 are divisible by 5.  Continue reading