Question

What is the smallest number by which 1328 may be multiplied so that the product is a perfect cube

Answer 1

SOLUTION

TO DETERMINE

The smallest number by which 1328 may be multiplied so that the product is a perfect cube

EVALUATION

$\sf{1328}$

$= \sf{2 \times 2 \times 2 \times 2 \times 83}$

$= \sf{ {2}^{3} \times 2 \times 83}$

In order to get the smallest number by which 1328 may be multiplied so that the product is perfect cube is

$= \sf{ {2}^{2} \times {83}^{2} }$

So the transformed number is

$= \sf{ {2}^{3} \times {2}^{3} \times {83}^{3} }$

Hence the required number

$= \sf{ {2}^{2} \times {83}^{2} }$

$= 27556$

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