A club has 26 girls and 39 boys as members the president wants to break the club and into groups with each group containing the same combination of girls and boys. The president also wants to make sure that no one has left out what is the greatest number of groups that the president can make

To solve this problem, we need to determine the greatest number of groups that can be formed such that each group contains the same combination of girls and boys, with no one left out. 

This is a greatest common divisor (GCD) problem, where we need to find the largest number of groups such that the number of girls and boys in each group is the same. The number of groups must divide both 26 (girls) and 39 (boys) evenly.

### Steps:

1. Find the greatest common divisor (GCD) of 26 and 39.
   
   - The prime factorization of 26 is \( 2 \times 13 \).
   - The prime factorization of 39 is \( 3 \times 13 \).

   The common factor between 26 and 39 is 13.

2. The greatest common divisor (GCD) of 26 and 39 is 13.

Thus, the president can make 13 groups, with each group containing:
- \( \frac{26}{13} = 2 \) girls
- \( \frac{39}{13} = 3 \) boys

### Answer:
The greatest number of groups the president can make is **13**.

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Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find the GCD of two numbers using the Euclidean algorithm?
2. What if the club had 30 girls and 42 boys? How many groups could be made?
3. Can the GCD method be applied when dividing members of a club with more than two categories (e.g., girls, boys, and non-binary members)?
4. What is the difference between GCD and least common multiple (LCM)?
5. How can prime factorization help in finding the GCD of larger numbers?

**Tip:** The GCD helps in splitting resources evenly, especially in situations involving divisibility and equal distribution.

A club has 26 girls and 39 boys as members. The president wants to break the club into groups, with each group containing the same combination of girls and boys. The president also wants to make sure that no one is left out. What is the greatest number of groups that the president can make?

Learn how to determine the greatest number of groups that can be formed from 26 girls and 39 boys using the Greatest Common Divisor (GCD) method. This problem demonstrates the use of prime factorization and the Euclidean algorithm for finding the GCD. Suitable for students in Grades 6-8.

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