Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package into plastic containers. She wants to divide the cookies into identical containers so that each container has the same number of each kind of cookie. If she wants each container to have the greatest number of cookies possible, how many plastic containers does she need?

To solve this problem, we need to find how many identical containers Kiara can use, each containing the greatest number of cookies. This means we need to divide both the 30 oatmeal cookies and the 48 chocolate chip cookies into the greatest number of containers, where each container holds the same number of each kind of cookie.

The solution involves finding the **greatest common divisor (GCD)** of 30 and 48, as this will give us the largest number of containers she can use, while ensuring each container has the same number of cookies.

### Step 1: Find the prime factorizations of 30 and 48.

- Prime factorization of 30:  
  \( 30 = 2 \times 3 \times 5 \)
  
- Prime factorization of 48:  
  \( 48 = 2^4 \times 3 \)

### Step 2: Identify the common factors.
The common factors between 30 and 48 are \( 2 \times 3 \).

### Step 3: Multiply the common factors to find the GCD.
The greatest common divisor (GCD) of 30 and 48 is:
\[
GCD(30, 48) = 2 \times 3 = 6
\]

### Step 4: Determine the number of containers.
Since the GCD is 6, this means Kiara can divide the cookies into 6 containers.

### Step 5: Verify how many cookies each container will have.
- Oatmeal cookies per container:  
  \( \frac{30}{6} = 5 \) oatmeal cookies per container.
  
- Chocolate chip cookies per container:  
  \( \frac{48}{6} = 8 \) chocolate chip cookies per container.

Thus, each container will have 5 oatmeal cookies and 8 chocolate chip cookies.

### Conclusion:
Kiara needs **6 plastic containers** to divide the cookies into the greatest number of identical containers.

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 Kiara had 45 oatmeal cookies and 60 chocolate chip cookies? How many containers would she need?
3. How is the least common multiple (LCM) of two numbers calculated, and when is it used?
4. How can you use prime factorization to solve other problems in mathematics?
5. How would the solution change if Kiara wanted each container to hold a different number of cookies?

**Tip:** When dealing with division problems involving groups or sets, always consider using the greatest common divisor (GCD) to find the optimal solution.

Learn how to divide 30 oatmeal cookies and 48 chocolate chip cookies into identical containers using the greatest common divisor (GCD). This step-by-step guide teaches GCD, prime factorization, and how to calculate the number of containers. Perfect for students in Grades 6-8.

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