Find the smallest number by which 7776 is to be divided to get a perfect square.

Given: 

Given number is $7776$.

To find: 

Here, we have to find the smallest number by which $7776$ has to be divided to get a perfect square.

Solution:

First of all, we will find the prime factors of $7776$.

$7776 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 $

$7776 = 2^5 \times 3^5$

$7776 = (2^2 \times 3^2)^2 \times 2 \times 3$

As we can see, if we divide the number $7776$ by $2 \times 3$, then the number will become a perfect square.

$\frac{7776}{6} = 1296$

$1296 = (4 \times 9)^2$

$1296 = (36)^2$

$1296$ is the square of $36$.

Therefore, $7776$ has to be divided by $6$ to obtain a perfect square.