Which of the following are perfect cube?166375 - Vidyadip

Question

Which of the following are perfect cube?166375

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Answer

On factorising 166375 into prime factors, we get
166375 = 5 × 5 × 5 × 11 × 11 × 11
Group the factors in triples of equal factors as:
166375 = {5 × 5 × 5} × {11 × 11 × 11}
It is evident that the prime factors of 166375 can be grouped into triples of equal factors and no factor is left over.
Therefore, 166375 is a perfect cube.

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