There are 144 boys and 132 girls in a class. These students are arranged in rows for prayer in such a way that each row has either boys or girls and every row has an equal number of students. Find the minimum number of rows in which all the students can be arranged

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Solution

The correct option is C 23
The number of students in each row will be the HCF of $144$ and $132$
First we write all numbers as product of their prime numbers.
So, $144 = 2^{4} \times 3^{2}$
$132 = 2^{2} \times 3 \times 11$
So, HCF $= 2^{2} \times 3 = 4 \times 3 = 12$
Total number of students $= 144 + 132 = 276$
So, with $12$ students in each row, number of rows $= \frac{276}{12} = 23$

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There are 144 boys and 132 girls in a class. These students are arranged in rows for prayer in such a way that each row has either boys or girls and every row has an equal number of students. Find the minimum number of rows in which all the students can be arranged

The correct option is C 23The number of students in each row will be the HCF of 144 and 132First we write all numbers as product of their prime numbers. So, 144=24×32132=22×3×11So, HCF =22×3=4×3=12Total number of students =144+132=276So, with 12 students in each row, number of rows =27612=23