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

##### 1 Answer

Mar 30, 2016

#### Answer:

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 = 2 xx 2 xx 2 xx 7#

#84 = 2 xx 2 xx 3 xx 7#

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

**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 / 70 = 1# with remainder#42#

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

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

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

So