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

Given, a number as 8640. We need to find out a number which if divided by the given number we get quotient as a perfect cube.

Step 1: Resolve 8640 into prime factors

We get, 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3 × 3 × 3

Step 2: Pair the factors obtained in the group of three

⇒ (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × 5

Step 3: divide the number with the factor which is alone.

Here, 2, 3 is in group of three and 5 is alone.

⇒ = 1728

Hence, 5 is the smallest number which is to be divided to the given number for perfect cube.