Find the smallest number by which 2808 must be multiplied so that the product is a perfect cube.

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169

144

125

100

answer is A.

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Detailed Solution

Concept: The problem at hand involves cubes and cube roots. Let the multiplier for the number be k. Therefore,

must be a flawless cube. Put a number in terms of the product of its prime elements to find the cube root of that number. This is how prime factorization is done.
Using prime factorisation method 2808

Multiples of three are known to be powers of prime factors in a perfect cube. Here, there are three twos, three threes, and one thirteen. For 2808 to be a perfect cube, we must add another

to the factorization.
In order to create a perfect cube, 2808 must be multiplied by the fewest number possible.

Hence, the correct option is 1.

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