Question

With what least number must 8640 be divided so that the quotient is a perfect cube?

• A. 5
• B. 15
• C. 6
• D. 10

Answer 1

The correct option is A

5

Prime factorization of 8640 is
$=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 5$
$=(2\times 2\times 2)\times (2\times 2\times 2)\times (3\times 3\times 3)\times 5$

For perfect cube, prime factor should form triplet.

Here, we can see all 2's and 3's are forming a triplet, but 5 does not.

Clearly, 8640 must be divided by 5, to make it a perfect cube.

After dividing by 5, we get 1728 as a quotient, which is a perfect cube.