Question

What is the smallest number by which 14641 must be divided so the quotient become a perfect square

Answer 1

A “perfect cube” is an integer that has an integer value as the “cube root”. The easiest and simplest way to find the answer is to cube small integer numbers starting with the smallest one, which is number “1”. When we get to 7 cubed, (or 7 x 7 x 7), the resulting perfect cube is 343.

Since the quotient of 1715 divided by 343 is 5, then the quotient of 1715 divided by 5 is 343, which is the perfect cube. In other words, 1715 should be divided by 5 (the smallest number) so that the quotient is a perfect cube (343).

I used a simple spreadsheet (3-columns, 5-rows) to solve this problem that I have available upon request.