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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
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2xy is the greatest common factor of the three monomials.

Step-by-step explanation:

There are three monomials such that greatest common factor of first and third monomial is 2xy and greatest common factor of second and third monomial is 2x²y.

As we know greatest common factor means, common prime factors of two numbers or expressions.

Greatest common factors of 1st and second and greatest common factors of 2nd and third monomials have been given.

So, common prime factors of these two greatest common factors will be greatest common factor of all three monomials.

Prime factors of 2xy = (2)(x)(y)

Prime factors of 2x²y = (2)(x)(x)(y)

So common factors are (2)(x)(y) which is the greatest common factors of all three monomials.