Question

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

704

Answer 1

2	704
2	352
2	176
2	88
2	44
2	22
11	11
	1

704 = 2 × 2 × 2 × 2 × 2 × 2 × 11

Here, one 11 is left, which is not a triplet.

If we divide 704 by 11, then it will become a perfect cube.

Thus, 704 ÷ 11

= 64

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

Hence, the smallest number by which 704 should be divided to make it a perfect cube is 11.