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Question

Find the smallest number by which the following number must be divided to obtain a perfect cube: 81


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Solution

Calculate the prime factorisation of 81.

81=3×3×3×3

To make it a perfect cube, it should be divided by 3.

813=3×3×3×33=3×3×3=27

which is a perfect cube of 3.

Hence, the smallest number by which 81 must be divided to obtain a perfect cube is 3.


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