What is the smallest number by which 3087 must be divided, so that the quotient is a perfect cube?

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answer is B.

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Detailed Solution

It is required to find the smallest number by which 3087 must be divided, so that the quotient is a perfect cube.
Now, using prime factorization and grouping the factors in triple form, represent the provided number as a product of prime factors.

⇒ 3087 = 3 × 3 × 7 × 7 × 7 = 32 × 73

We observe that just two 3s appear in the prime factorization of 3087. So, 3087 must be divided by 9 so that the quotient is a perfect cube.
So, the fewest number by which 3087 must be divided to produce a quotient that is an exact cube is 9.
Therefore, option 2 is correct.

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