What is the smallest number by which 1600
Question:

What is the smallest number by which 1600 must be divided so that the quotient is a perfect cube?

Solution:

1600

1600 can be expressed as the product of prime factors in the following manner:

$1600=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \times 5$

Therefore, to make the quotient a perfect cube, we have to divide 1600 by:

$5 \times 5=25$