A school has 391 boys and 323 girls. They are to be divided into the largest possible number of identical classes so that each class has the same number of boys and the same number of girls. How many classes are formed, and how many boys and girls are in each class?

Introduction / Context:
This item focuses on using the highest common factor (HCF) to form the maximum number of identical classes from two groups. The number of classes must divide each of the two populations so that every class has the same count of boys and the same count of girls.

Given Data / Assumptions:

• Boys = 391.
• Girls = 323.
• All classes must be identical with equal composition.

Concept / Approach:
If the number of classes is k, then k must divide both 391 and 323. The largest possible number of classes is thus k = HCF(391, 323). Then the number of boys per class is 391 / k and the number of girls per class is 323 / k.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Only option B correctly states both the number of classes (17) and the per-class composition (23 boys, 19 girls). The others swap labels or give incorrect class counts.

Common Pitfalls:

• Mistaking “23 classes” for “23 per class”, or mixing the counts of boys and girls per class.

Final Answer: