Becky wants to display 20 photos and 8 drawings she owns in groups, with each group having the same combination of photos and drawings and none left over. What is the greatest number of groups Becky can display?


To solve this problem, we need to find how many groups Becky can form where each group has the same combination of photos and drawings without leaving any photos or drawings left over. This means we are looking for the greatest number of groups in which both the 20 photos and the 8 drawings can be evenly divided.

This is a typical greatest common divisor (GCD) problem, where we need to find the GCD of 20 and 8.

### Steps to find the GCD:
1. List the factors of 20:
   - \( 20 = 1, 2, 4, 5, 10, 20 \)

2. List the factors of 8:
   - \( 8 = 1, 2, 4, 8 \)

3. The common factors are \( 1, 2, 4 \), and the greatest common divisor is **4**.

### Conclusion:
The greatest number of groups Becky can display is **4**. In each group, there will be:
- \( \frac{20}{4} = 5 \) photos,
- \( \frac{8}{4} = 2 \) drawings.

Would you like further details on the steps, or have any questions?

Here are 5 related questions to explore:
1. What if Becky had 30 photos and 12 drawings?
2. How do you find the least common multiple (LCM) of two numbers?
3. What if Becky only wants groups of 3 drawings?
4. How would the solution change if Becky had 22 photos and 8 drawings?
5. Can this approach be used for grouping other items like books or paintings?

**Tip:** When solving grouping or arrangement problems, finding the GCD helps determine the largest equal groups possible!

Becky wants to display 20 photos and 8 drawings she owns in groups, with each group having the same combination of photos and drawings and none left over. What is the greatest number of groups Becky can display?

Discover how to solve the problem of grouping 20 photos and 8 drawings equally using the Greatest Common Divisor (GCD). This step-by-step guide teaches how to apply number theory concepts like GCD and the Euclidean algorithm, ideal for students in Grades 5-7.

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