The least number by which 72 be divided

Question:

The least number by which 72 be divided to make it a perfect cube, is________

Solution:

 9

Resolving 72 into prime factors, we get

72=2 x 2 x 2 x 3 x 3

Grouping the factors in triplets of equal factors, we get

72 = (2 x 2 x 2) x 3 x 3

Clearly, if we divide 72 by 3 x 3, the quotient would be 2 x 2 x 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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