Question

Which of the following is  perfect cube? 

166375

Answer 1

On factorising 166375 into prime factors, we get:

\[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\]

Group the factors in triples of equal factors as:

\[166375 = \left\{ 5 \times 5 \times 5 \right\} \times \left\{ 11 \times 11 \times 11 \right\}\]

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.