Question

Find the smallest number by which of the following number must be multiplied to obtain a perfect cube.

675

Answer 1

3	675
3	225
3	75
5	25
5	5
	1

675 = 3 × 3 × 3 × 5 × 5

Here, two 5s are left, which are not in a triplet. To make 675 a cube, one more 5 is required.

Then, we obtain

675 × 5 = 3 × 3 × 3 × 5 × 5 × 5 = 3375 is a perfect cube.

Hence, the smallest natural number by which 675 should be multiplied to make it a perfect cube is 5.