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Greatest Common Factor of Monomials

To find the greatest common factor of two monomials, first find the prime factorization of each monomial, including all the variables (and a 1 factor if necessary).

Then take the product of all common factors.


Find the GCF of:

27 p 2 q r 5


15 p 3 r 3

First, find the prime factorization of each monomial.

27 p 2 q r 5 = 1 3 3 3 p p q r r r r r 15 p 3 r 3 = 3 5 p p p r r r

Common factors are shown in red. Their product is:

3 p p r r r

So, the GCF is 3 p 2 r 3 .
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