Critical thinking challenges like this one can be as much a part of a math class as learning concepts, computations, and formulas.

## Challenge:

What is the smallest positive integer *p* such that 1080*p* is a perfect cube number?

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The correct answer is 25.

First, find the factor of 1080p. The prime factors of 1080p are:

\(2^3×3^3×5×p\)

In order for \(2^3×3^3×5×p\) to be a perfect cube, each prime factor must come in sets of triples. Since, we have \(2^3×3^3×5\), thus, we only need to change 5 to \(5^3\). Therefore, p equals to \(5^2\) or 25.