Question

Which of the following is  perfect cube? 

3087

Answer 1

On factorising 3087 into prime factors, we get:

\[3087 = 3 \times 3 \times 7 \times 7 \times 7\]

Group the factors in triples of equal factors as:

\[3087 = 3 \times 3 \times \left\{ 7 \times 7 \times 7 \right\}\]

It is evident that the prime factors of 3087 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 243 is a not perfect cube.