Consider an integer y that possesses precisely three positive divisors, including 1 and y itself. What is the total number of positive divisors of y^3?

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Official Explanation

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An integer y with exactly three positive divisors must be of the form p^2, where p is a prime number. The divisors of y are 1, p, and p^2. When we calculate y^3, we have (p^2)^3 = p^6. The number of positive divisors of p^6 can be found…

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Comments

SankariJan 19, 2025

Great!

DhruvFeb 24, 2025

this pattern comes up frequently

SmritiFeb 19, 2025

thanks

What this question tests

What it tests

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

Common trap

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