Question

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

135

Answer 1

3	135
3	45
3	15
5	5
	1

135 = 3 × 3 × 3 × 5

Here, one 5 is left, which is not in a triplet.

If we divide 135 by 5, then it will become a perfect cube.

Thus, 135 ÷ 5 = 27

= 3 × 3 × 3 is a perfect cube.

Hence, the smallest number by which 135 should be divided to make it a perfect cube is 5.