# 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?

$11.99 Satisfied 123 Students 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. ### More math articles ### What people say about "Algebra Puzzle - Critical Thinking 15"? No one replied yet. X 30% OFF Limited time only! Save Over 30% SAVE$5

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