Question

A teacher wants to arrange maximum possible numbers of 6000 students in a field such that the number of rows is equal to the number of columns. Find the number of rows if 71 were left out after the arrangement. [4 MARKS]

Answer 1

Concept : 1 Mark
Prime factorisation : 2 Marks
Conclusion : 1 Mark

Since 71 students were left, so remaining students = 6000 - 71 = 5929

$\therefore$ Prime factorization of 5929

$\begin{array}{cc}7& 5929\\ 7& 847\\ 11& 121\\ 11& 11\\ & 1\end{array}$

$\therefore 5929=7\times 7\times 11\times 11$

$\sqrt{5929}=7\times 11=77$

Hence, the required number of rows = 77