Question

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

Answer 1

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`