Question

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

Answer 1

Question:-

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

Answer :-

53240 / 2 = 26620

26620 / 2 = 13310

13310 / 2 = 6655

6655 / 5 = 1331

1331 / 11 = 121

121 / 11 = 11

11 / 11 = 1

Only sets of 3 numbers is 2 and 11, and remainder is 5.

53240 = 5 * 22^2

Divide the number by 5 so that the quotient is a perfect cube.

If we divided the number by 5, then the prime factorisation of the quotient will not contain 5. 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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