Question

A teacher wants to arrange 2,800 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 96 were left out after the arrangement.

Answer 1

$\text{Number of students who participated}\text{in the arrangement}=2,800-96=2,704$

$\text{On prime factorizing 2,704, we get,}$

$\begin{array}{cc}2& 2,704\\ 2& 1,352\\ 2& 676\\ 2& 338\\ 13& 169\\ 13& 13\\ & 1\end{array}$

$2,704=2\times 2\times 2\times 2\times 13\times 13$

$\sqrt{2,704}=2\times 2\times 13=52$

$\text{Hence, the required number of}\text{rows}=52$