Question

Find if the following number is not a perfect cube? 

243

Answer 1

On factorising 243 into prime factors, we get:

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

On grouping the factors in triples of equal factors, we get:

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

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.

Thus, 243 is the required number, which is not a perfect cube.