Question

In inter school compititions there are 120 girls and 140 boys and have to be arranged in rows such that each row have equal number of students and contains only either boys or girls. What can be the maximum number of students in each row?

• A. 2
• B. 10
• C. 60
• D. 20

Answer 1

The correct option is D 20

Given,
Total number of girls = 120
Total number of boys = 140
To get maximum number of students in each row, we have to find GCD of 120 and 140.

$\underset{–}{\text{Prime factrorization of 120:}}$

$\begin{array}{cc}2& 120\\ 2& 60\\ 3& 30\\ 5& 10\\ & 2\end{array}$

$\therefore 120=2\times 2\times 3\times 5\times 2$

$\underset{–}{\text{Prime factrorization of 140:}}$

$\begin{array}{cc}2& 140\\ 2& 70\\ 7& 35\\ & 5\end{array}$

$\therefore 140=2\times 2\times 7\times 5$

We get, GCD by multiplying common terms in the prime factorization of 120 and 140.

$\therefore$ GCD of 120 and 140 $=2\times 2\times 5=20$