Question

Which of the following is  perfect cube? 

 456533

 

Answer 1

On factorising 456533 into prime factors, we get:

\[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\]

Group the factors in triples of equal factors as:

\[456533 = 7 \times 7 \times 7 \times 11 \times 11 \times 11\]

It is evident that the prime factors of 456533 can be grouped into triples of equal factors and no factor is left over. Therefore, 456533 is a perfect cube.