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