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Question

There are three monomials such that the greatest common factor of the first and second monomials is 2xy, and the greatest common factor of the second and third monomials is 2x2y.
The greatest common factor of the three monomials is what

Answer 1

First monomial has factors:                    2xy         *           (something else #1)

 

Second monomial has factors:                2xy   *   2    *        (something else #2)

 

"the greatest common factor of the first and second monomials is 2xy"

 

Third monomial has factors:                        2x2y     *     (something else #3)

 

"the greatest common factor of the second and third monomials is 2x2y"

 

The GCF of all three:                              2xy

Answer 2

If the greatest common factor of the 1st and 2nd is 2xy and the greatest common factor of the 2nd and 3rd is 2x2y, in total we have a GCF which includes a constant, 2, twice, an x and a y.

 

The GCF of the 3 monomials is 2x2y