# Algebra Puzzle – Critical Thinking 15

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 1080p is a perfect cube number?

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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.

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