Question

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

192

Answer 1

2	192
2	96
2	48
2	24
2	12
2	6
3	3
	1

192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

Here, one 3 is left, which is not in a triplet.

If we divide 192 by 3, then it will become a perfect cube.

Thus, 192 ÷ 3 = 64

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

Hence, the smallest number by which 192 should be divided to make it a perfect cube is 3.