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What is the smallest number by which 8192 must be divided so that quotient is a perfect cube ? Also, find the cube root of the quotient so obtained.
We have to find the smallest number by which 8192 must be divided so that quotient is a perfect cube and find the cube root of the product.
Prime factorisation of 8192 is,
Grouping the factors in triplets of equal factors, we see that $2$ is left.
In order to make 8192 a perfect cube, we have to divide it by $2$.
The smallest number by which 8192 must be divided so that the quotient is a perfect cube is 2 and the cube root of the quotient is 16.
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