Question

What is the smallest number by which 8640 must be divided so that the quotient is a perfect cube? [2 Marks]

Answer 1

In order to find the smallest number to be divided first we factorize 8640.
⇒8640=2×2×2×2×2×2×3×3×3×5 [1 Mark]

⇒8640=2^6× 3^3 ×5 In the above factorization, we find that there is a triplet of 2 and 3 but there is no triplet of 5.

Hence, 5 is the smallest number which must divide 8640 so that the quotient is a perfect cube.
[1 Mark]