Question

Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

Answer 1

Given: 9720

Factors of 9720 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5

As we see, 3 and 5 do not have a pair to make a cube.

Hence 9720 should be divided with 3 × 3 × 5 to get perfect cube.

⇒ 9720 should divide with 45.

Now, after division we get 216 = 6³

Now, 216 is a perfect cube.