Question

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

256

Answer 1

2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

∴ 256 is not a perfect cube

Here, two 2s are left, which are not in a triplet. To make 256 a cube, one more 2 is required.

Then, we obtain

256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 is a perfect cube.

Hence, the smallest natural number by which 256 should be multiplied to make it a perfect cube is 2.