Students can practice identifying common factors by filling out these Venn diagrams for pairs of numbers such as 12 and 16.

Absolutely! Let’s solve Section A of this worksheet: *Finding the GCF (Greatest Common Factor) using Venn Diagrams*.

The key idea is:
- List all factors of each number.
- Place common factors in the overlapping section of the Venn diagram.
- The GCF is the largest number in that overlapping section.

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🔢 Problem 1: Factors of 12 and 6

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 6: 1, 2, 3, 6

✔ Common factors (overlap): 1, 2, 3, 6
➡️ GCF = 6

Venn Diagram Fill:
- Left circle (only 12): 4, 12
- Overlap: 1, 2, 3, 6
- Right circle (only 6): *(none — all factors of 6 are also factors of 12)*

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🔢 Problem 2: Factors of 12 and 16

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 16: 1, 2, 4, 8, 16

✔ Common factors (overlap): 1, 2, 4
➡️ GCF = 4

Venn Diagram Fill:
- Left circle (only 12): 3, 6, 12
- Overlap: 1, 2, 4
- Right circle (only 16): 8, 16

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🔢 Problem 3: Factors of 10 and 5

Factors of 10: 1, 2, 5, 10
Factors of 5: 1, 5

✔ Common factors (overlap): 1, 5
➡️ GCF = 5

Venn Diagram Fill:
- Left circle (only 10): 2, 10
- Overlap: 1, 5
- Right circle (only 5): *(none — all factors of 5 are also factors of 10)*

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🔢 Problem 4: Factors of 15 and 20

Factors of 15: 1, 3, 5, 15
Factors of 20: 1, 2, 4, 5, 10, 20

✔ Common factors (overlap): 1, 5
➡️ GCF = 5

Venn Diagram Fill:
- Left circle (only 15): 3, 15
- Overlap: 1, 5
- Right circle (only 20): 2, 4, 10, 20

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🔢 Problem 5: Factors of 9 and 18

Factors of 9: 1, 3, 9
Factors of 18: 1, 2, 3, 6, 9, 18

✔ Common factors (overlap): 1, 3, 9
➡️ GCF = 9

Venn Diagram Fill:
- Left circle (only 9): *(none — all factors of 9 are also factors of 18)*
- Overlap: 1, 3, 9
- Right circle (only 18): 2, 6, 18

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🔢 Problem 6: Factors of 18 and 24

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

✔ Common factors (overlap): 1, 2, 3, 6
➡️ GCF = 6

Venn Diagram Fill:
- Left circle (only 18): 9, 18
- Overlap: 1, 2, 3, 6
- Right circle (only 24): 4, 8, 12, 24

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## ✔ Final Answers for Section A:

| Pair | GCF |
|--------------|-----|
| 12 and 6 | 6 |
| 12 and 16 | 4 |
| 10 and 5 | 5 |
| 15 and 20 | 5 |
| 9 and 18 | 9 |
| 18 and 24 | 6 |

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## 🧠 Explanation Summary:

- GCF = Greatest Common Factor → the largest number that divides both numbers evenly.
- Venn Diagram Method helps visualize which factors are shared.
- The intersection (overlap) of the two circles contains all common factors.
- Pick the biggest number from that overlap → that’s your GCF!

This method is especially helpful for visual learners and builds a strong foundation for understanding LCM (Least Common Multiple) later on.

Let me know if you’d like help with Section B (LCM) next! 😊