Is 2880 a perfect cube? If not, by which smallest natural number should 2880 be divided so that the quotient is a perfect cube?

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answer is C.

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Detailed Solution

Concept- To solve this problem, we will multiply the integers that are not in pairs of three, divide 2880 by the result, and then multiply the result by the LCM of 2880.
The prime factors of 2880 are

.
Primes of 3 and 5 do not appear in pairs of three. Thus, 2880 is not a perfect cube.
The prime 3 and prime 5 both appear only twice in the factorization of 2880.
Thus, if we divide 2880 by

then the prime factorization of the quotient will not consist of 3 and 5.
Therefore, the smallest natural number by which 2880 should be divided to make it a perfect cube is 75
Hence, the correct answer is option (3).

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