ISEE Mathematics Achievement Question 316: Answer and Explanation

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Question: 316

16. What is the greatest common factor of (3xy)³ and 3x²y⁵ ?

A. xy
B. 3x²y⁵
C. 3x²y³
D. 27x³y³

Correct Answer: C

Explanation:

C First, simplify the first expression: (3xy)³ = 3³x³y³ = 27x³y³. While comparing it to the other expression, 3x²y⁵, you can work in bite-sized pieces. Start with the coefficients: the greatest common factor of 3 and 27 is 3. Eliminate (A) and (D) since those don't contain 3. Both of the remaining answers contain x², so compare y in the two expressions. One has y³ = y × y × y and the other has y⁵ = y × y × y × y × y. The greatest common factor is y³ since both expressions have at least 3 y's. Eliminate (B). The correct answer is (C).

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