Question

The least number by which 72 be divided to make it a perfect cube is ______.

Answer 1

The least number by which 72 be divided to make it a perfect cube is 9.

Explanation:

Resolving 72 into prime factors, we get

72 = 2 × 2 × 2 × 3 × 3

Grouping the factors in triplets of equal factors, we get

72 = (2 × 2 × 2) × 3 × 3

Clearly, if we divide 72 by 3 × 3, the quotient would be 2 × 2 × 2, which is a perfect cube.

Hence, the least number by which 72 be divided to make it, a perfect cube, is 9.