Question

What is a smallest number by which $2560$ is to be multiplied so that the product is a perfect cube?

Answer 1

The given number ends with $0$ therefore it is divisible by $2$ and $5$.

Thus,

$2560=\underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times \underset{–}{2\times 2\times 2}\times 5$

From the factors, we can say that only $5$ is a factor that is not occurring three times or in the multiple of it to make it a perfect cube.

So to make it a perfect cube, the above number should be multiplied with $5\times 5=25.$

So, $25$ is the required answer.