Math worksheet for finding HCF using Venn diagrams.

Let's solve Section A of the worksheet step by step. The goal is to:

1. List all factors of each number.
2. Complete the Venn diagram by placing shared factors in the overlapping region and unique factors in their respective circles.
3. Identify the HCF (Highest Common Factor) — this is the product of the numbers in the intersection (overlap) of the two circles.

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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: 1, 2, 3, 6 → These go in the overlap
Only in 12: 4, 12
Only in 6: None (all factors are shared)

✔ HCF of 12 and 6 = 6

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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 → Go in the overlap
Only in 12: 3, 6, 12
Only in 16: 8, 16

✔ HCF of 12 and 16 = 4

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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 → Overlap
Only in 10: 2, 10
Only in 5: None

✔ HCF of 10 and 5 = 5

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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 → Overlap
Only in 15: 3, 15
Only in 20: 2, 4, 10, 20

✔ HCF of 15 and 20 = 5

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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 → Overlap
Only in 9: None
Only in 18: 2, 6, 18

✔ HCF of 9 and 18 = 9

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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 → Overlap
Only in 18: 9, 18
Only in 24: 4, 8, 12, 24

✔ HCF of 18 and 24 = 6

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## ✔ Final Answers:

| Pair | HCF |
|------|-----|
| 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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📌 How to Use Venn Diagrams for HCF:

- Place common factors in the intersection.
- Place unique factors in the non-overlapping parts.
- The HCF is the product of numbers in the intersection, but since we're listing factors, it's just the largest common factor (which is already the maximum in the overlap).

> 💡 Tip: You can also find HCF using prime factorization, but Venn diagrams help visualize shared factors clearly!

Let me know if you'd like me to draw the filled-in Venn diagrams or help with LCM next!