ISEE Word Problems Question 257: Answer and Explanation

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Question: 257

6. If p and q are prime numbers, what is the greatest common factor of 4p⁸q and 10p⁵q⁴ ?

A. 2p⁸q
B. 2p⁵q⁴
C. 2p⁵q
D. 20p⁸q⁴

Correct Answer: C

Explanation:

Begin with the coefficients. As the factors of 4 are 1, 2, and 4, and the factors of 10 are 1, 2, 5, 10, the greatest common factor is 2. As p⁵ is a factor of p⁸, the greatest common factor of p⁵ and p⁸ is p⁵. As q is a factor of q⁴, the greatest common factor of q and q⁴ is q.

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