What is the greatest common factor of 30 and 42?

To find the greatest common factor of two monomials that are just numbers like 30 and 42, we can start by setting up a factor tree for each of those numbers.

Our next step is to take a look a look at those factor trees and find the factors that are in common to both numbers. Notice that both numbers have a factor of 3 and both numbers also have a factor of 2. Once you have found the factors that match up, you want to multiply those factors together to get the greatest common factor of the two numbers. Since the number 3 matches up and the number 2 matches up, the greatest common factor would be 6.

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