Question

By which smallest number must the following number be divided so that the quotient is a perfect cube?

8788

Answer 1

On factorising 8788 into prime factors, we get:

\[8788 = 2 \times 2 \times 13 \times 13 \times 13\]

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

\[8788 = 2 \times 2 \times \left\{ 13 \times 13 \times 13 \right\}\]

It is evident that the prime factors of 8788 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 8788 is a not perfect cube. However, if the number is divided by (\[2 \times 2 = 4\]), the factors can be grouped into triples of equal factors such that no factor is left over.

 

Thus, 8788 should be divided by 4 to make it a perfect cube.