Divisibility rules are especially useful if you are trying to quickly perform a prime factorization of a number. They can save you the necessity of punching numbers into a calculator, if you can use them quickly. Learning these rules is a great enrichment activity for math students.

Probably the most commonly known divisibility rule is the divisibility rule for 2. How do you know if a number is divisible by 2? Easy! If it's even, it's divisible by 2. Or, to put it another way, if it ends in 0, 2, 4, 6, or 8.

But what about 4? How can you tell if a number is divisible by 4? Well, it's actually almost as easy as the divisibility rule for 2. Instead of looking at the last digit, you look at the last 2 digits. Are they divisible by 4? Then the whole number is! For example, 224 is divisible by 4 because 24 is. But 4566 is not, because 66 is not.

And 8? Well, for 8, you look at the last three digits, and ask yourself, "Is this divisible by eight?" So 5024 is divisible by 8 because 024 is divisible by 8. Needless to say, this isn't quite as quick and easy as the 4 rule or the 2 rule, but...

Here's a hint that helps out with the 8 rule a little: if the last two digits are divisible by 4, and the third-to-last digit is even, then the number is divisible by 8.

And last but not least - you can generalize! A number is divisible by 2n if the last n digits are divisible by 2n.