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What is the greatest common factor of 4x^2y and 6xy^3?
AGCF = 2xy^3
BGCF = 12xy
CGCF = 2x^2y
DGCF = 2xy
Answer & Solution
Correct answer: D. GCF = 2xy
1. Factor the coefficients into primes: 4 = 2 times 2, and 6 = 2 times 3.
2. Write the variables in expanded form: the first expression has x times x times y, and the second has x times y times y times y.
3. The shared factors are one 2 from the coefficients, one x, and one y, since the first expression only offers a single y.
4. Multiply the common factors together: 2 times x times y gives 2xy.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 7 "Factoring", section 7.1 Greatest Common Factor and Factor by Grouping_
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