Question

Find the smallest number which when it divides $2048$, the quotient is a perfect square.

Answer 1

To find the smallest number by which 2048 must be divided so that the quotient is a perfect square, we have to find the prime factors of 9408.

$2048=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$

Prime factors of 2048 are $2,2,2,2,2,2,2,2,2,2,2$.

Out of the prime factors of 2048, only one 2 is without a pair.

So, 2 is the number by which 2048 must be divided to make the quotient a perfect square.

$\Rightarrow \frac{2048}{2}=1024$

$\sqrt{1024}=32$

Hence, the smallest number is 2, which when divides 2048, the quotient is 1024 which is a perfect square.

Hence, the correct answer is 2.