Question

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

243

Answer 1

3	243
3	81
3	27
3	9
3	3
	1

243 = 3 × 3 × 3 × 3 × 3

∴ 243 is not a perfect cube.

Here, two 3s are left that are not in a triplet. To make 243 a cube, one more 3 is required.

In that case, 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 = 729 is a perfect cube.

Hence, the smallest natural number by which 243 should be multiplied to make it a perfect cube is 3.