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Method 1:

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Factor the each monomial.

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a2b3 = a · a · b · b · b

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ab3 a · b · b · b

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The GCF is the product of the common prime factors in each monomial.

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GCF =  a · b · b · b

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The greatest common factor of a2b3 and ab3 is ab3.\"\"

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The greatest common factor of a2b3 and ab3 is ab3.