How do you find the GCF of 20 and 28?

Question

Riley Anderson · Accepted Answer

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

These are some techniques (in no particular order), each with pros and cons for various types of examples.

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

The GCF of two positive whole numbers can be found in the following manner:

That is their GCF if the numbers are identical to one another.

If not, repeat with the larger number substituted with the smaller number's subtracted value.

In our illustration:

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

The GCF of two positive whole numbers can be found in the following manner:

To find the remainder and quotient, divide the larger number by the smaller one.

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

If not, repeat with the remainder and the smaller number.

Thus, in our instance:

#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

Determine the prime factorizations of two positive whole numbers, then multiply the common factors by two to get the GCF of those two numbers.

In our illustration:

#20 = 2*2*5#

#28=2*2*7#

Thus, the GCF is:

#2*2 = 4#

Levi Adams · Answer

undefined To find the greatest common factor (GCF) of 20 and 28, you can use the method of prime factorization. Find the prime factors of each number and then identify the common prime factors. Multiply these common prime factors together to obtain the GCF.