Divisibility tests

Last updated: 9 Jul 2008

Remember you will not have a calculator in the GMAT.

So when you are looking for factors of a number, either because that is explicitly asked of you in a question or you are simplifying a fraction then the following tests will be useful.

Divisible by 2

Every number which ends with 0, 2, 4, 6 or 8 is divisible by 2, and is therefore an even number.

For example:

• 258 ends in the number '8' and therefore is divisible by 2.
• 1783 ends in the number '3' and is therefor not divisible by 2

Divisible by 3

If the sum of the digits in a number is divisible by 3 then the number is divisible by 3.

For example:

• The sum of the digits in 105 is 6 which is divisible by 3 so 105 is divisible by 3.
• The sum of the digits in 236 is 11 which is not divisible by 3 so 236 is not divisible by 3.

Divisible by 4

If the last 2 digits of the number are divisible by 4 then the whole number is divisible by 4.

For example

• The last two digits of 932 are '32' which is divisible by 4 so 932 is divisible by 4.
• The last two digits of 1014 are '14' which is not divisible by 4 so 1014 is not divisible by 4.

Divisible by 5

If the last digit of a number is 0 or 5 then the number is divisible by 5.

For example:

• The last digit of 1025 is '5' therefore 1025 is divisible by 5.
• The last digit of 324 is '4' therefore 324 is not divisible by 5.

Tip: Dividing by 5 is the same as multiplying by 2 and then dividing by 10. However multiplying by 2 and then dividing by 10 is much easier for most people to do without a calculator.

For example what is 235 divided by 5?

235 x 2 is 470. 470 divided by 10 is 47.

Therefore 235 divided by 5 is 47.

Divisible by 6

To be divisible by 6 a number must be divisible by 2 and by 3, so if it passes both these earlier tests then it is divisible by 6. I.e. the last digit is 0, 2, 4, 6 or 8 and the sum of the digits is divisible by 3.

Divisible by 7

I am afraid that about the easiest way to check for divisibility by 7 is to do the long division.

Divisible by 8

If the last 3 digits of the number are divisible by 8 then the whole number is divisible by 8.

• The last 3 digits of 12408 are '408' which is divisible by 8 therefore 12408 is divisible by 8.
• The last 3 digits of 13014 are '014' which is not divisible by 8 so 13014 is not divisible by 8.

Divisible by 9

If the sum of the digits is divisible by 9 then the number is divisible by 9.

For example:

• The sum of the digits in 378 is 18 which is divisible by 9 therefore 378 is divisible by 9.
• The sum of the digits in 1563 is 15 which is not divisible by 9 so 1563 is not divisible by 9.

Next page: Summary of properties of numbers