Question

The smallest number by which 7623 must be divided to get a perfect square is .

• A. 7
• B. 9
• C. 11

Answer 1

The correct option is A 7

$\text{Prime factorization of 7623:}$
$$\begin{array}{cc}3& 7623\\ 3& 2541\\ 11& 847\\ 11& 77\\ & 7\end{array}$$
$\therefore 7623=\underset{–}{3\times 3}\times \underset{–}{11\times 11}\times 7$
$=3^2\times {11}^2\times 7$
Here, 7 is not paired.
So, 7623 when divided by 7 gives $3^2\times {11}^2$ which is a perfect square.

Therefore, the smallest number by which 7623 must be divided to get a perfect square is 7.