Math worksheet for finding the greatest common factor (GCF) using Venn diagrams, featuring six pairs of numbers.

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.
- Put common factors in the overlapping part (intersection) of the Venn diagram.
- The GCF is the largest number in that intersection.

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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 (intersection): 1, 2, 3, 6
➡️ GCF = 6

Venn Diagram Filling:
- 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: 1, 2, 4
➡️ GCF = 4

Venn Diagram Filling:
- Left (only 12): 3, 6, 12
- Overlap: 1, 2, 4
- Right (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: 1, 5
➡️ GCF = 5

Venn Diagram Filling:
- Left (only 10): 2, 10
- Overlap: 1, 5
- Right (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: 1, 5
➡️ GCF = 5

Venn Diagram Filling:
- Left (only 15): 3, 15
- Overlap: 1, 5
- Right (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: 1, 3, 9
➡️ GCF = 9

Venn Diagram Filling:
- Left (only 9): (none — all factors of 9 are also factors of 18)
- Overlap: 1, 3, 9
- Right (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: 1, 2, 3, 6
➡️ GCF = 6

Venn Diagram Filling:
- Left (only 18): 9, 18
- Overlap: 1, 2, 3, 6
- Right (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) is the largest number that divides both numbers evenly.
- Using a Venn diagram, we visually separate unique and shared factors.
- The overlap contains all common factors — the biggest one there is the GCF.
- This method helps students see *why* the GCF is what it is — not just memorize a number.

You can now confidently fill in the Venn diagrams and write the correct GCF for each pair!

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