A total of 672 boys and 480 girls are on a national learning trip. The boys and the the girls are to be divided into separate smaller groups such that each group has the same number of girls and boys. What is the in each group such that no student is left out? maximum number of students

To find the maximum number of students in each group such that no student is left out and each group contains the same number of boys and girls, we need to determine the greatest common divisor (GCD) of the number of boys (672) and the number of girls (480). The GCD will give us the largest number of students per group that can be evenly divided from both the boys and the girls.

### Steps:
1. **Find the GCD of 672 and 480.**
   We can use the Euclidean algorithm to find the GCD:
   
   - Divide 672 by 480 and find the remainder:
     \[
     672 \div 480 = 1 \quad \text{remainder} \, 192
     \]
   - Now, divide 480 by 192:
     \[
     480 \div 192 = 2 \quad \text{remainder} \, 96
     \]
   - Divide 192 by 96:
     \[
     192 \div 96 = 2 \quad \text{remainder} \, 0
     \]
   Since the remainder is 0, the GCD is **96**.

2. **Number of boys and girls in each group**:
   - Each group will have 96 students, with 96 boys and 96 girls.

Thus, the maximum number of students in each group, such that no student is left out and each group has an equal number of boys and girls, is **96**.

### Further explanation or questions?
Here are five questions to expand your understanding:
1. How can the Euclidean algorithm be used to find the GCD of other numbers?
2. Why is the GCD important for dividing groups in this kind of problem?
3. What would happen if the number of boys and girls were not divisible by the GCD?
4. Can you explain how to extend this method to cases with more than two groups?
5. How can the concept of LCM (Least Common Multiple) be used in problems involving combining groups?

**Tip**: The Euclidean algorithm is a fast and efficient way to find the GCD, even for large numbers!

A total of 672 boys and 480 girls are on a national learning trip. The boys and the girls are to be divided into separate smaller groups such that each group has the same number of girls and boys. What is the maximum number of students in each group such that no student is left out?

This problem involves dividing 672 boys and 480 girls into smaller equal groups with the same number of boys and girls, using the greatest common divisor (GCD). Learn how to apply the Euclidean algorithm to find the maximum number of students per group, ensuring no student is left out. Suitable for students in Grades 6-8.

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