Consider a positive integer n such that the t… | GMAT Sprint

Free Practice Question

PS · Problem Solving

605-655

Divisibility/Multiples/Factors

Consider a positive integer n such that the total count of positive divisors of $7^n$ equals 16. How many positive divisors does $8^n$ have?

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Official Explanation

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Let n be a positive integer such that the number of positive factors of

7^n

is 16. The formula for the number of positive factors of

p^n

n + 1

, where

p

is a prime number. Therefore, we have

n + 1 = 16

, which gives us

n = 15

. Now, we need to find…

Comments

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What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.