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To solve this problem, we need to divide the 16 fifth graders and 36 sixth graders into teams such that each team has the same number of fifth and sixth graders, with the greatest possible number of teams.

### Step 1: Find the Greatest Common Factor (GCF)
1. The number of fifth graders is 16.
2. The number of sixth graders is 36.

The GCF of 16 and 36 will give us the greatest number of teams Coach Matt can make, with each team having an equal number of fifth and sixth graders.

#### Finding the GCF of 16 and 36:
- The factors of 16 are: 1, 2, 4, 8, 16.
- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36.
  
The greatest common factor between 16 and 36 is **4**.

So, Coach Matt can make **4 teams**.

### Step 2: Determine the Number of Students per Team
To find out how many fifth and sixth graders each team will have, divide the number of each grade by 4 (the number of teams).

- Fifth graders per team: \( \frac{16}{4} = 4 \)
- Sixth graders per team: \( \frac{36}{4} = 9 \)

### Answer
- Coach Matt can make **4 teams**.
- Each team will have **4 fifth graders** and **9 sixth graders**.

Would you like more details or have any questions?

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Here are some related questions to explore:
1. What if Coach Matt had 18 fifth graders and 42 sixth graders?
2. How does finding the GCF help in creating balanced teams?
3. Can we apply the GCF method to split different groups fairly?
4. What if Coach Matt wanted fewer teams with more students per team?
5. How would the problem change if there were an odd number of students?

**Tip:** The GCF helps determine the largest number of equal groups you can create with two or more sets.

Coach Matt is making dodgeball teams. He has 16 fifth graders and 36 sixth graders. To be fair, Coach Matt wants there to be the same number of fifth graders and the same number of sixth graders on each team. What is the greatest number of teams Coach Matt can make using all the students? How many fifth graders and sixth graders will each team have?

Learn how to solve a problem involving the Greatest Common Factor (GCF) by dividing 16 fifth graders and 36 sixth graders into equal teams. This solution explores the concepts of GCF and division, providing a step-by-step approach for sixth-grade students.

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