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# 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#