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Question

Question 46

Fill in the blanks to make the statements true.

The least number by which 72 be multiplied to make it a perfect cube is ___.


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Solution

3
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
We find that 2 occurs as a prime factor of 72 thrice, but 3 occurs as a prime factor only twice. Thus, if we multiply 72 by 3, 3 will also occur as a prime factor thrice and the product will be 2×2×2×3×3×3, which is a perfect cube.
Hence, the least number, which should be multiplied by 72 to get a perfect cube is 3.


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