Question

Which of the following is  perfect cube? 

 106480

Answer 1

On factorising 106480 into prime factors, we get:

\[106480 = 2 \times 2 \times 2 \times 2 \times 5 \times 11 \times 11 \times 11\]

Group the factors in triples of equal factors as:

\[106480 = \left\{ 2 \times 2 \times 2 \right\} \times 2 \times 5 \times \left\{ 11 \times 11 \times 11 \right\}\]

It is evident that the prime factors of 106480 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 106480 is a not perfect cube.