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

Mar 30, 2016

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:

$56 = 2 \times 2 \times 2 \times 7$

$84 = 2 \times 2 \times 3 \times 7$

$G C F \left(56 , 84\right) = 2 \times 2 \times 7 = 28$

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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 $70$:

$\frac{112}{70} = 1$ with remainder $42$

$\frac{70}{42} = 1$ with remainder $28$

$\frac{42}{28} = 1$ with remainder $14$

$\frac{28}{14} = 2$ with remainder $0$

So $G C F \left(112 , 70\right) = 14$