Question

The smallest natural number by which $1296$ be divided to get a perfect cube is ______.

• A. $16$
• B. $6$
• C. $60$
• D. none of these

Answer 1

Answer: (B)

The correct option is B $6$

Prime factorising $1296$, we get,

$1296=2\times 2\times 2\times 2\times 3\times 3\times 3\times 3$

$=2^4\times 3^4$.

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

Here, number of $2$'s is $4$ and number of $3$'s is $4$.

So we need to divide $2$ and $3$ from the factorization to make $1296$ a perfect cube.

Hence, the smallest number by which $1296$ must be divided to obtain a perfect cube is $2\times 3=6$.

Therefore, option $B$ is correct.