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?
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Solution: 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 divided 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.
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