Mary is packing snacks for a trip. She has 72 pretzel rods and 48 string cheese. What is the largest number of bags she can make so that all the bags are all the same and there is nothing left over?

To determine the largest number of bags Mary can make so that each bag has the same number of pretzel rods and string cheese without any leftovers, we need to find the **Greatest Common Divisor (GCD)** of 72 (pretzel rods) and 48 (string cheese).

1. **Prime factorization of 72:**
   - \(72 = 2^3 \times 3^2\)
   
2. **Prime factorization of 48:**
   - \(48 = 2^4 \times 3^1\)

3. **Find the GCD:**
   - The GCD is found by taking the lowest power of all common prime factors.
   - For \(2\), the lowest power is \(2^3\).
   - For \(3\), the lowest power is \(3^1\).

   So, the GCD is:
   \[
   \text{GCD} = 2^3 \times 3^1 = 8 \times 3 = 24
   \]

The greatest number of bags Mary can make is **24**. Each bag will have:
- \( \frac{72}{24} = 3 \) pretzel rods
- \( \frac{48}{24} = 2 \) string cheese

Would you like more details or have any questions?

Here are 5 related questions you might find interesting:
1. How would the result change if Mary had 90 pretzel rods and 60 string cheese?
2. What if Mary wanted to pack 36 bags instead? How many pretzel rods and string cheese would each bag contain?
3. Can you explain how the prime factorization method works in finding the GCD?
4. What other methods could be used to find the GCD?
5. How can Mary adjust her packing if she decides to use half the number of pretzel rods?

**Tip:** When finding the GCD of two numbers, prime factorization provides a clear view of the common factors between them.

Discover how to determine the largest number of bags Mary can make with 72 pretzel rods and 48 string cheese, ensuring each bag has the same number of items without leftovers. Learn about number theory concepts like the Greatest Common Divisor (GCD) and prime factorization method. Suitable for Grades 6-8.

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