How do you find the GCF of 20 and 28?
1 Answer
Answer:
The GCF of
Explanation:
Here are a few methods (in no particular order). Each method has its advantages and disadvantages in different kinds of examples.
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#2820 = 8# to get:#color(blue)(20, 8)# 
Replace
#20# with#208 = 12# to get:#color(blue)(12, 8)# 
Replace
#12# with#128=4# to get:#color(blue)(4, 8)# 
Replace
#8# with#84=4# to get:#color(blue)(4, 4)# 
So the GCF is
#color(blue)(4)#
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
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#