Question

Find the smallest number by which 10985 should be divided so that the quotient is a perfect cube

Answer 1

5	10985
13	2197
13	169
13	13
	1

We have 10985 = 5 × 13 × 13 × 13

= 5 × 13 × 13 × 13

Here we have a triplet of 13 and we are left over with 5.

If we divide 10985 by 5, the new number will be a perfect cube.

∴ The required number is 5.