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Question

Find the smallest number by which 1715 be divided so that the quotient is a perfect cube


A

1

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B

7

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C

5

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D

Already a perfect cube

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Solution

The correct option is C

5


For a number to be a perfect cube, its prime factors should be expressed as triplets.
By prime factorization, we get 1715=7×7×7×5

We have three 7’s but only one 5 so we need to divide the number by 5.
We need to divide it by 5, then it becomes cube of 7 i.e 343


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