Question

Find the smallest number by which 8640 must be divided so that quotient is a perfect cube

Answer 1

Here is your answer,

8640 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5

5 occurs as a prime factor only one

Hence 5 is the smallest number by which 8640 must be divided so that the quotient is a perfect cube