Question

625,Find the smallest number by which the given number must be divided to obtain a perfect cube.

Answer 1

after dividing we get 125 which is perfect cube

Answer 2

The smallest number by which the given number must be divided to obtain a perfect cube is 5.

Step-by-step explanation:

We are given a number 625 and we have to find the smallest number by which this number must be divided to obtain a perfect cube.

Firstly, we will find do the prime factorization of the given number 625, that means;

625  =  5 $\times$ 125

125  =  5 $\times$ 25

25  =  5 $\times$ 5

5  =  5 $\times$ 1

At the last step we get 1 as quotient so we will stop doing our procedures.

So, factorization of 625 = 5 $\times$ 5 $\times$ 5 $\times$ 5

Now, as we know that for making this number a perfect cube we need three 5 which means we have to eliminate one 5 from it so that it becomes a perfect cube.

This means that the smallest number by which 625 must be divided to obtain a perfect cube is 5 because only then we get a number 125 which is a perfect cube of 5.