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If , then which number should be divided by to get a perfect cube.

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answer is A.

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Detailed Solution

Concept: The next step is to express the supplied number as the product of powers of prime factors, after which we will compare it to any number's general form, which is a perfect cube.
Given data,

Let's use the prime factorization of the provided integer

to represent it.

In order for a number to be a perfect cube, it must have the form

, where

, and

are the provided number's prime factors and

, and

are any other numbers. In other words, the prime factors' powers must all be multiples of

.
It is obvious that the provided number

can be expressed as follows in the above form:
Question Image

A perfect cube,

, is equivalent to

in the equation above, hence the provided number,

, needs to be divided by

to produce a perfect cube.
Hence, the correct answer is option (1).

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