Question

Is $250$ a perfect cube? If not, then by which smallest natural number should $250$ be divided so that the quotient is a perfect cube?

Answer 1

Prime factorising, $250=2\times \underset{}{5\times 5\times 5}$.

We know, a perfect cube has multiples of $3$ as powers of prime factors.

The prime factor $2$ does not appear in triplet form.

Therefore, $250$ is not a perfect cube.

Since in the factorization, $2$ appears only one time, we must divide the number $250$ by $2$, then the quotient is a perfect cube.

$\therefore 250÷2=125$

$=5\times 5\times 5=5^3$, which is a perfect cube.

$\therefore$ The smallest number by which $250$ should be divided to make it a perfect cube is $2$.