Question : In a school, 391 boys and 323 girls have been divided into the largest possible equal classes, so that each class of boys numbers the same as each class of girls. What is the number of classes?
Option 1: 23
Option 2: 19
Option 3: 42
Option 4: 17
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Correct Answer: 42
Solution :
Given: 391 Boys and 323 Girls in the class.
Prime factors of 391 = (17 × 23)
Prime factors of 323 = (17 × 19)
HCF of (391, 323) = 17
The largest possible equal number of students in each class = 17
Now, find the number of classes of boys when there are 391 boys
$⇒\frac{391}{17}=23$
Similarly, the number of classes of girls when there are 323 girls,
$⇒ \frac{323}{17}=19$
Then, total number of classes = (23 + 19) = 42
Hence, the correct answer is 42.
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