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There are 144 boys and 132 girls in a class. These students ar

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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

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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

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Text solutionVerified

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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Question Text	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
Answer Type	Text solution:1
Upvotes	150

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

Text solutionVerified

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