By what smallest number should 1,350 be divided so that the quotient is a perfect cube?

Explanation

1. 01

   $1{,}350 = 2 \times 3^3 \times 5^2$.

2. 02

   For a cube every power must be a multiple of 3; $3^3$ is fine, but 2 and $5^2$ are not.

3. 03

   Divide by $2 \times 5^2 = 50$: $1{,}350 \div 50 = 27 = 3^3$.