Find the smallest number by which the given number must be multiplied so that the product become a perfect cube : 128

Given: A number $128$.

To do: To find the smallest number by which the given number must be multiplied so that the product become a perfect cube.

Solution:

Given number: $128$

On factorization,

$128=2\times2\times2\times2\times2\times2\times2$

$\Rightarrow 128=\underline{2\times2\times2}\times\underline{2\times2\times2}\times2$

$\Rightarrow 128=2^3\times2^3\times2$

Thus, number $128$ should be multiplied by $( 2\times2=4)$ to make it perfect cube.