Question

Which of the following is  perfect cube? 

243

Answer 1

On factorising 243 into prime factors, we get:

\[243 = 3 \times 3 \times 3 \times 3 \times 3\]

Group the factors in triples of equal factors as:

\[243 = \left\{ 3 \times 3 \times 3 \right\} \times 3 \times 3\]

It is evident that the prime factors of 243 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 243 is a not perfect cube.