# How can you find the greatest common factor of two

How can you find the greatest common factor of two numbers?
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Step 1
Factor both numbers into ' factors, identify the common factors and multiply them together.
For example, find the GCF of 56 and 84 as follows:
$56=2×2×2×7$
$84=2×2×3×7$
$GCF\left(56,84\right)=2×2×7=28$

Step 1
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 $GCF\left(112,70\right)=14$