Question

Find the smallest number by which 128 must be divided to obtain a perfect cube.

Answer 1

We have 128=2×2×2×2×2×2×2.
Grouping the prime factors of 128 into triples, we are left with 2.
Thus, 128 is not a perfect cube.
dividing by 2
64 = 2 × 2 × 2 × 2 × 2 × 2
i.e. 64 is a perfect cube.
∴ the smallest required number is 2.