Question

Find the smallest number by which each of the following number must be divided to obtain a perfect cube:
(i) $81$ (ii) $128$ (iii) $135$ (iv) $192$ (v) $704$ (vi) $625$

Answer 1

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

On prime factorising, we get:

(i) $81=3^4$.

$\therefore 81$ can be made a perfect cube by dividing it by $3$.

(ii) $128=2^7$.

$\therefore 128$ can be made a perfect cube by dividing it by $2$.

(iii) $135=3^3\times 5$.

$\therefore 135$ can be made a perfect cube by dividing it by $5$.

(iv) $192=2^6\times 3$.

$\therefore 192$ can be made a perfect cube by dividing it by $3$.

(v) $704=2^6\times 11$.

$\therefore 704$ can be made a perfect cube by dividing it by $11$.

(vi) $625=5^4$.

$\therefore 625$ can be made a perfect cube by dividing it by $5$.