Question

Is $1188$ a perfect cube? If not, by which smallest natural number should it be divided so that the quotient is a perfect cube?

• A. $44$
• B. $33$
• C. $22$
• D. $11$

Answer 1

The correct option is A $44$

Prime factorising $1188$, we get,

$1188=2\times 2\times 3\times 3\times 3\times 11$

$=2^2\times 3^3\times 11$.

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

Here, number of $2$'s is $2$, number of $3$'s is $3$ and number of $11$'s is $1$.

So we need to divide $2^2$ and $11$ from the factorization to make $1188$ a perfect cube.

Hence, the smallest number by which $1188$ must be divided to obtain a perfect cube is $2^2\times 11=44$.

Therefore, option $A$ is correct.