Question

What is the greatest common factor for 12 and 15?

Answer 1

`3`

Explanation:

The GCF of `12` and `15` is `3`.

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One way to find this is to break down these two numbers into their prime factorisations:

`12 = 2 xx 2 xx 3`

`15 = 3 xx 5`

We see that the only common factor (greater than `1`) is `3`, so that is the greatest common factor. If the two numbers had more than one prime factor in common, you would multiply them together to find the GCF.

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Another method, which does not require us to factor both of the numbers first goes as follows:

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Divide the larger number by the smaller number to give a quotient and remainder.

If the remainder is zero then the smaller number is the GCF.

Otherwise repeat with the smaller number and the remainder.

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In our example:

`15 / 12 = 1` with remainder `3`

`12 / 3 = 4` with remainder `0`

So the GCF is `3`.