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Question

Find the smallest number which when multiplied with 53240 will make the product a perfect cube.

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Solution

Here the prime factors if the given number
53240=2×2×2×5×11×11×11

As we know that a cube of a number consists of product of three similar numbers.
in the above factors we find that there is a triplet of 2 and 11, but not of 5.

To make a triplet for 5 we need two more 5
=5×5
=25

So, the required number is 25.

53240×25=1331000


1331000 is perfect cube of 110.


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