Question

Find the smallest number by which each of thr following number must be multiplied ot obtain a perfect cube for 6517

Answer 1

Answer:

Find the smallest number by which 68600 must be multiplied to get a perfect cube.

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Solution



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Correct option is

A

5

Prime factorising 68600, we get,

68600=2×2×2×5×5×7×7×7

          =23×52×73.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, number of 2's is 3, number of 5's is 2 and number of 7's is 3.

So we need to multiply another 5 in the factorization to make 68600 a perfect cube.

Hence, the smallest number by which 68600 must be multiplied to obtain a perfect cube is 5.