Finding HCF and LCM - Including the Use of Venn Diagrams Worksheet ... - Free Printable

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

#### Step 1: List factors
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 6: 1, 2, 3, 6

#### Step 2: Fill Venn Diagram
- Overlap (common factors): 1, 2, 3, 6
- Only in 12: 4, 12
- Only in 6: (none — all factors are shared)

#### Step 3: HCF
The highest common factor is the largest number in the overlap:
✔ HCF = 6

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🔹 Problem 2: Factors of 12 and 16

#### Step 1: List factors
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 16: 1, 2, 4, 8, 16

#### Step 2: Fill Venn Diagram
- Overlap (common): 1, 2, 4
- Only in 12: 3, 6, 12
- Only in 16: 8, 16

#### Step 3: HCF
Largest common factor:
✔ HCF = 4

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🔹 Problem 3: Factors of 10 and 5

#### Step 1: List factors
- Factors of 10: 1, 2, 5, 10
- Factors of 5: 1, 5

#### Step 2: Fill Venn Diagram
- Overlap: 1, 5
- Only in 10: 2, 10
- Only in 5: (none)

#### Step 3: HCF
✔ HCF = 5

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🔹 Problem 4: Factors of 15 and 20

#### Step 1: List factors
- Factors of 15: 1, 3, 5, 15
- Factors of 20: 1, 2, 4, 5, 10, 20

#### Step 2: Fill Venn Diagram
- Overlap: 1, 5
- Only in 15: 3, 15
- Only in 20: 2, 4, 10, 20

#### Step 3: HCF
✔ HCF = 5

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🔹 Problem 5: Factors of 9 and 18

#### Step 1: List factors
- Factors of 9: 1, 3, 9
- Factors of 18: 1, 2, 3, 6, 9, 18

#### Step 2: Fill Venn Diagram
- Overlap: 1, 3, 9
- Only in 9: (none — all are shared)
- Only in 18: 2, 6, 18

#### Step 3: HCF
✔ HCF = 9

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🔹 Problem 6: Factors of 18 and 24

#### Step 1: List factors
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

#### Step 2: Fill Venn Diagram
- Overlap: 1, 2, 3, 6
- Only in 18: 9, 18
- Only in 24: 4, 8, 12, 24

#### Step 3: HCF
✔ HCF = 6

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✔ Final Answers Summary:

| 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 the Venn Diagram:

- Left circle: Factors of first number (only those not shared)
- Right circle: Factors of second number (only those not shared)
- Middle (overlap): Common factors
- HCF = Largest number in the overlap

This method helps visualize which factors are shared and makes finding the HCF intuitive.

Let me know if you'd like a visual version of these diagrams!