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 ___.

Answer 1

9
Resolving 72 into prime factors, we get
$72=2\times 2\times 2\times 3\times 3$
Grouping the factors in triplets of equal factors, we get
$72=(2\times 2\times 2)\times 3\times 3$
Clearly, if we divide 72 by $3\times 3$, the quotient would be $2\times 2\times 2$, which is a perfect cube.
Hence, the least number by which 72 be divided to make it a perfect cube is 9.