GCF Using Venn Diagram Worksheets - Free Printable
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Step-by-step solution for: GCF Using Venn Diagram Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: GCF Using Venn Diagram Worksheets
Absolutely! Let’s solve each problem step by step using Venn diagrams to find the Greatest Common Factor (GCF) of each pair of numbers.
The GCF is the largest number that divides both numbers evenly. Using a Venn diagram, we:
- List all factors of the first number in one circle.
- List all factors of the second number in the other circle.
- The overlap (intersection) contains the common factors.
- The largest number in the overlap is the GCF.
---
a) Complete the Venn diagram:
- Factors of 7: 1, 7
- Factors of 21: 1, 3, 7, 21
Venn Diagram:
- Left circle (Factors of 7): 7
- Right circle (Factors of 21): 3, 21
- Overlap (Common factors): 1, 7
*(Note: 1 is always a common factor, so it goes in the overlap too.)*
b) Common factors: 1, 7
c) GCF(7, 21) = 7
✔ *Explanation:* Since 7 is a factor of 21, the GCF is 7.
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a) Complete the Venn diagram:
- Factors of 8: 1, 2, 4, 8
- Factors of 16: 1, 2, 4, 8, 16
Venn Diagram:
- Left circle (Factors of 8): (nothing unique — all factors are shared)
- Right circle (Factors of 16): 16
- Overlap (Common factors): 1, 2, 4, 8
b) Common factors: 1, 2, 4, 8
c) GCF(8, 16) = 8
✔ *Explanation:* 8 divides 16 evenly, so GCF is 8.
---
a) Complete the Venn diagram:
- Factors of 15: 1, 3, 5, 15
- Factors of 9: 1, 3, 9
Venn Diagram:
- Left circle (Factors of 15): 5, 15
- Right circle (Factors of 9): 9
- Overlap (Common factors): 1, 3
b) Common factors: 1, 3
c) GCF(15, 9) = 3
✔ *Explanation:* The largest number that divides both 15 and 9 is 3.
---
a) Complete the Venn diagram:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 14: 1, 2, 7, 14
Venn Diagram:
- Left circle (Factors of 12): 3, 4, 6, 12
- Right circle (Factors of 14): 7, 14
- Overlap (Common factors): 1, 2
b) Common factors: 1, 2
c) GCF(12, 14) = 2
✔ *Explanation:* Only 1 and 2 divide both numbers; 2 is the largest.
---
a) Complete the Venn diagram:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 4: 1, 2, 4
Venn Diagram:
- Left circle (Factors of 24): 3, 6, 8, 12, 24
- Right circle (Factors of 4): (nothing unique — all are shared)
- Overlap (Common factors): 1, 2, 4
b) Common factors: 1, 2, 4
c) GCF(24, 4) = 4
✔ *Explanation:* Since 4 divides 24, the GCF is 4.
---
a) Complete the Venn diagram:
- Factors of 6: 1, 2, 3, 6
- Factors of 3: 1, 3
Venn Diagram:
- Left circle (Factors of 6): 2, 6
- Right circle (Factors of 3): (nothing unique)
- Overlap (Common factors): 1, 3
b) Common factors: 1, 3
c) GCF(6, 3) = 3
✔ *Explanation:* 3 divides 6, so GCF is 3.
---
## ✔ Final Answers:
| Problem | Common Factors | GCF |
|---------|----------------------|---------|
| 1) 7,21 | 1, 7 | 7 |
| 2) 8,16 | 1, 2, 4, 8 | 8 |
| 3) 15,9 | 1, 3 | 3 |
| 4) 12,14| 1, 2 | 2 |
| 5) 24,4 | 1, 2, 4 | 4 |
| 6) 6,3 | 1, 3 | 3 |
Let me know if you’d like to visualize the Venn diagrams drawn out too!
The GCF is the largest number that divides both numbers evenly. Using a Venn diagram, we:
- List all factors of the first number in one circle.
- List all factors of the second number in the other circle.
- The overlap (intersection) contains the common factors.
- The largest number in the overlap is the GCF.
---
1) 7, 21
a) Complete the Venn diagram:
- Factors of 7: 1, 7
- Factors of 21: 1, 3, 7, 21
Venn Diagram:
- Left circle (Factors of 7): 7
- Right circle (Factors of 21): 3, 21
- Overlap (Common factors): 1, 7
*(Note: 1 is always a common factor, so it goes in the overlap too.)*
b) Common factors: 1, 7
c) GCF(7, 21) = 7
✔ *Explanation:* Since 7 is a factor of 21, the GCF is 7.
---
2) 8, 16
a) Complete the Venn diagram:
- Factors of 8: 1, 2, 4, 8
- Factors of 16: 1, 2, 4, 8, 16
Venn Diagram:
- Left circle (Factors of 8): (nothing unique — all factors are shared)
- Right circle (Factors of 16): 16
- Overlap (Common factors): 1, 2, 4, 8
b) Common factors: 1, 2, 4, 8
c) GCF(8, 16) = 8
✔ *Explanation:* 8 divides 16 evenly, so GCF is 8.
---
3) 15, 9
a) Complete the Venn diagram:
- Factors of 15: 1, 3, 5, 15
- Factors of 9: 1, 3, 9
Venn Diagram:
- Left circle (Factors of 15): 5, 15
- Right circle (Factors of 9): 9
- Overlap (Common factors): 1, 3
b) Common factors: 1, 3
c) GCF(15, 9) = 3
✔ *Explanation:* The largest number that divides both 15 and 9 is 3.
---
4) 12, 14
a) Complete the Venn diagram:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 14: 1, 2, 7, 14
Venn Diagram:
- Left circle (Factors of 12): 3, 4, 6, 12
- Right circle (Factors of 14): 7, 14
- Overlap (Common factors): 1, 2
b) Common factors: 1, 2
c) GCF(12, 14) = 2
✔ *Explanation:* Only 1 and 2 divide both numbers; 2 is the largest.
---
5) 24, 4
a) Complete the Venn diagram:
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 4: 1, 2, 4
Venn Diagram:
- Left circle (Factors of 24): 3, 6, 8, 12, 24
- Right circle (Factors of 4): (nothing unique — all are shared)
- Overlap (Common factors): 1, 2, 4
b) Common factors: 1, 2, 4
c) GCF(24, 4) = 4
✔ *Explanation:* Since 4 divides 24, the GCF is 4.
---
6) 6, 3
a) Complete the Venn diagram:
- Factors of 6: 1, 2, 3, 6
- Factors of 3: 1, 3
Venn Diagram:
- Left circle (Factors of 6): 2, 6
- Right circle (Factors of 3): (nothing unique)
- Overlap (Common factors): 1, 3
b) Common factors: 1, 3
c) GCF(6, 3) = 3
✔ *Explanation:* 3 divides 6, so GCF is 3.
---
## ✔ Final Answers:
| Problem | Common Factors | GCF |
|---------|----------------------|---------|
| 1) 7,21 | 1, 7 | 7 |
| 2) 8,16 | 1, 2, 4, 8 | 8 |
| 3) 15,9 | 1, 3 | 3 |
| 4) 12,14| 1, 2 | 2 |
| 5) 24,4 | 1, 2, 4 | 4 |
| 6) 6,3 | 1, 3 | 3 |
Let me know if you’d like to visualize the Venn diagrams drawn out too!
Parent Tip: Review the logic above to help your child master the concept of lcm using venn diagrams.
