Question

By which smallest number should 42592 be divided so that the quotient is a perfect cube?

Answer 1

Step 1: Find the prime factorisation of 42592.

$\begin{array}{cc}2& 42592\\ 2& 21296\\ 2& 10648\\ 2& 5324\\ 2& 2662\\ 11& 1331\\ 11& 121\\ 11& 11\\ & 1\end{array}$

$42592=(2\times 2\times 2)\times 2\times 2\times (11\times 11\times 11)$

Step 2: Find the factor which is not in triplets

• Here prime factor $11$ appears in triplets but prime factor $2$ appears five times which is not in triplets.

• This means if $42592$ is divided by $2\times 2$, then it would become a perfect cube.

Hence, $42592$ should be divided by $4$ so that the quotient is a perfect cube.