By which smallest number should 8788 be divided so that the quotient is a perfect cube?

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answer is A.

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Detailed Solution

It is given that 8788 must be divided by the smallest number so that the quotient is a perfect cube.
Find the prime factorization of 8878.

28788243941321971316913131

Prime factorization of

8788 = 2 × 2 × 13 × 13 × 13 ¯ .

From the prime factorization, it’s concluded that prime factor 2 doesn’t occur in triplet form but, factor 13 occurs in a triplet. From the information, it’s given that for the product to be a perfect cube; all the prime factors should exist in the triplet.
To make it a perfect cube, the prime factors that aren’t occurring in triplets must be eliminated.
To complete the triplet number, 8788 needs to be divided by

2 × 2

that is 4.
Hence, the smallest number by which 8788 must be divided so that the quotient becomes a perfect cube is 4.
Thus, option (1) is correct.

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