What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?

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answer is C.

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Detailed Solution

Concept- In order to solve this question, we will first factor the given number, which will give a few factors. Next, we will arrange these factors into groups of three because the number must be a perfect cube, and the number that remains will be the correct response.
We need to determine the smallest integer by which 1600 must be divided in order for the result to be a perfect cube.
We will start by factoring the given integer, which is 1600.
The result of factoring the number is

Then, we get the factors of 1600. However, as the question identifies that the answer must be a perfect cube, we will now group the numbers in a group of three.
We can observe that the number 5 does not form a triplet, because it consists of only two 5’s.
Therefore, the number

or 25 must be divided in order for the result to be a perfect cube.
However, 25 is the smallest number by which 1600 must be divided in order for the quotient to be a perfect cube.
Hence, the correct answer is an option 3).

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