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Question

By which smallest number 8788 must be divided so that quotient is a perfect cube

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Solution

The given number is 8788

The prime factorisation of 8788 is given by,

8788=2×2×13×13×13

We see that prime factor 2 does not occur in the group of 3, hence the given number is not a perfect cube.

In order to make it a perfect cube, it must be divided by 4.

Now, 87884=2×2×13×13×134

2197=13×13×13, which is a perfect cube number.

Thus, the cube root of 2197=13

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