Question

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

Answer 1

5 is the smallest number that 8640 must be divided with so that the quotient is a perfect cube.

Step-by-step explanation:

As we know,

Prime Factorization of 8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5

= $2^{3}$ * $2^{3}$ * $3^{3}$ * 5

In this factorization, the triplets of 2 and 3 but not of 5.

So,

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

Learn more: find the least number divisible

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