What is the greatest common factor for 12 and 15?

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What is the greatest common factor for 12 and 15?

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Answer 1 · 2016-04-10T09:06:13

$3$ $3$

Explanation:

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

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

$12 = 2 \times 2 \times 3$ $12 = 2 xx 2 xx 3$

$15 = 3 \times 5$ $15 = 3 xx 5$

We see that the only common factor (greater than $1$ $1$ ) is $3$ $3$ , 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:

$\frac{15}{12} = 1$ $15 / 12 = 1$ with remainder $3$ $3$

$\frac{12}{3} = 4$ $12 / 3 = 4$ with remainder $0$ $0$

So the GCF is $3$ $3$ .

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What is the greatest common factor for 12 and 15?

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