Divisibility Tests

There are some rules that you can use to quickly check if a number is divisible by any number from two to twelve. We can call these divisibility tests. There are some that are not that useful, such as seven and eleven. For those particular numbers, you will probably find it just as simple to figure it out by just simply doing the division. But for the rest of the numbers, there are some very helpful hints.

Divisibility by two: If the last digit of the number is divisible by two, then the whole number is divisible by two.

Divisibility by three: Take the sum of all the digits of a number, and if the sum is divisible by three, then the whole number is divisible by three.

Divisibility by four: When you look at the last two digits of a number, if that two-digit number is divisible by four, then the whole number is divisible by four. You would only have to look at the last two digits of a number because four is divided equally into one-hundred, so therefore you already know that you only have to focus on the last two digits.

Divisibility by five: If the last digit is a zero or five, then the whole number is divisible by five.

Divisibility by six: Because six is the result of two times three, if the number is divisible by two and by three, then the whole number is divisible by six.

Divisibility by eight: When you look at the last three digits off a number, if that three-digit number is divisible by eight, then the whole number is divisible by eight. You would only have to look at the last three digits of a number because eight is divided equally into one-thousand, so therefore you already know that you only have to focus on the last three digits.

Divisibility by nine: Take the sum of all the digits of the number, and if the sum is divisible by nine, then the whole number is divisible by nine.

Divisibility by ten: If the number ends in a zero, then the number is divisible by ten.

Divisibility by twelve: Because twelve is the result of three times four, if the number is divisible by three and by four, then the whole number is divisible by twelve.

These simple rules, if remember, will help you tremendously when dealing with larger numbers. It will help you break those numbers down into easier, and more manageable numbers to work with.