How can you find the greatest common factor of two numbers?

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How can you find the greatest common factor of two numbers?

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Answer 1 · 2016-03-30T18:50:32

Here are a couple of methods...

Explanation:

Method 1

Factor both numbers into prime factors, identify the common factors and multiply them together.

For example, find the GCF of $56$ and $84$ as follows:

$56 = 2 xx 2 xx 2 xx 7$

$84 = 2 xx 2 xx 3 xx 7$

$GCF(56, 84) = 2 xx 2 xx 7 = 28$

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Method 2

Given two numbers, divide the larger by the smaller to find a quotient and remainder. If the remainder is zero then the smaller number was the GCF. Otherwise, repeat with the smaller number and the remainder.

Example: find the GCF of $112$ and $70$ :

$112 / 70 = 1$ with remainder $42$

$70 / 42 = 1$ with remainder $28$

$42 / 28 = 1$ with remainder $14$

$28 / 14 = 2$ with remainder $0$

So $GCF(112, 70) = 14$

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How can you find the greatest common factor of two numbers?

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