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Question

Question 47

Fill in the blanks to make the statements true.

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=2×2×2×3×3
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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