How do you find the GCF of 20 and 28?

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Jan 12, 2017

Answer:

The GCF of #20# and #28# is #4#

Explanation:

Here are a few methods (in no particular order). Each method has its advantages and disadvantages in different kinds of examples.

#color(white)()#
Method 1 - Subtraction

Given two positive whole numbers, you can find their GCF as follows:

  • If the numbers are the same as one another then that is their GCF.

  • Otherwise, replace the larger number with the result of subtracting the smaller number from it and repeat.

In our example:

  • Given: #color(blue)(20, 28)#

  • Replace #28# with #28-20 = 8# to get: #color(blue)(20, 8)#

  • Replace #20# with #20-8 = 12# to get: #color(blue)(12, 8)#

  • Replace #12# with #12-8=4# to get: #color(blue)(4, 8)#

  • Replace #8# with #8-4=4# to get: #color(blue)(4, 4)#

  • So the GCF is #color(blue)(4)#

#color(white)()#
Method 2 - Division

Given two positive whole numbers, you can find their GCF as follows:

  • Divide the larger number by the smaller to give a quotient and remainder.

  • If the remainder is #0# then the smaller number is the GCF.

  • Otherwise, repeat with the smaller number and the remainder.

So in our example:

#28/20 = 1" "# with remainder #8#

#20/8 = 2" "# with remainder #4#

#8/4 = 2" "# with remainder #0#

So the GCF is #4#

#color(white)()#
Factoring

To find the GCF of two positive whole numbers, find their prime factorisations and multiply the common factors together.

In our example:

#20 = 2*2*5#

#28=2*2*7#

So the GCF is:

#2*2 = 4#

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