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To solve this problem, we need to determine the greatest number of groups the teacher can create where both boys and girls are equally distributed.

### Step 1: Identify the numbers
- Number of boys = 24
- Number of girls = 40

### Step 2: Calculate the Greatest Common Factor (GCF)
The greatest number of groups will be equal to the GCF of the number of boys and girls. This is because the GCF represents the largest number by which both the number of boys and girls can be divided evenly.

### Step 3: Find the GCF of 24 and 40
We can find the GCF by listing the factors of each number or using the prime factorization method:

- **Factors of 24**: 1, 2, 3, 4, 6, 8, 12, 24
- **Factors of 40**: 1, 2, 4, 5, 8, 10, 20, 40

The common factors are 1, 2, 4, and 8. The greatest of these is **8**.

### Conclusion
The greatest number of groups the teacher can create is **8**.

Would you like more details or have any questions about this solution?

Here are some related questions to consider:
1. How would the solution change if the number of boys was 30 and the number of girls remained 40?
2. What is the least common multiple (LCM) of 24 and 40, and what does it represent in this context?
3. How could the solution be adjusted if the teacher wanted groups of exactly 4 boys and 5 girls?
4. If the number of boys was 36 and the number of girls was 48, what would be the greatest number of groups?
5. How can prime factorization be used to find the GCF of any two numbers?

**Tip:** When solving problems involving equal distribution into groups, the greatest common factor (GCF) is often the key to finding the largest possible number of groups.

There are 24 boys and 40 girls in chorus. If the teacher wishes to create groups in which the boys and girls are equally distributed, what is the greatest number of groups he can create?

Discover how to find the greatest number of groups that can be formed with 24 boys and 40 girls in chorus using the Greatest Common Factor (GCF). This problem highlights key number theory concepts suitable for Grades 5-7 students.

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