Question

Is 53240 a perfect cube? If not, then by which smallest natural number should 53240 be divided so that the quotient is a perfect cube?

Answer 1

53240 = 2 × 2 × 2 × 11 × 11 × 11 × 5

The prime factor 5 does not appear in a group of three. So, 53240 is not a perfect cube. In the factorisation 5 appears only one time. If we divide the number by 5, then the prime factorisation of the quotient will not contain 5.

So, 53240 ÷ 5 = 2 × 2 × 2 × 11 × 11 × 11

Hence the smallest number by which 53240 should be divided to make it a perfect

cube is 5.

The perfect cube, in that case, is = 10648.