Question

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

Answer 1

it is not a perfect cube it should be divided by 5

Answer 2

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Solution:

53240 = 2 × 2 ×2 ×11 ×11× 11×5

The prime factor 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 factonsation of the quotient will not contain 5.

53240 + 5 = 2×2×2×11×

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