Let's solve the
"Finding the Greatest Common Factor (GCF)" worksheet step by step.
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🔷 Understanding the Task
We are to:
1. Find all
factors of each given number.
2. Then find the
greatest common factor (GCF) between two numbers in each pair.
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✔ Step 1: List Factors for Each Number
We'll list all factors for each number:
#### 1.
12
Factors:
1, 2, 3, 4, 6, 12
#### 2.
9
Factors:
1, 3, 9
#### 3.
20
Factors:
1, 2, 4, 5, 10, 20
#### 4.
30
Factors:
1, 2, 3, 5, 6, 10, 15, 30
#### 5.
22
Factors:
1, 2, 11, 22
#### 6.
77
Factors:
1, 7, 11, 77
#### 7.
27
Factors:
1, 3, 9, 27
#### 8.
25
Factors:
1, 5, 25
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✔ Step 2: Find GCF for Each Pair
Now, let’s compute the
GCF for each pair.
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#### 🔹 GCF(12, 9)
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 9: 1, 3, 9
- Common factors:
1, 3
- Greatest common factor:
3
✔ GCF(12, 9) = 3
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#### 🔹 GCF(12, 20)
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors:
1, 2, 4
- Greatest:
4
✔ GCF(12, 20) = 4
---
#### 🔹 GCF(12, 30)
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common factors:
1, 2, 3, 6
- Greatest:
6
✔ GCF(12, 30) = 6
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#### 🔹 GCF(12, 22)
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 22: 1, 2, 11, 22
- Common factors:
1, 2
- Greatest:
2
✔ GCF(12, 22) = 2
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#### 🔹 GCF(12, 77)
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 77: 1, 7, 11, 77
- Common factors:
1
- Greatest:
1
✔ GCF(12, 77) = 1
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#### 🔹 GCF(27, 25)
- Factors of 27: 1, 3, 9, 27
- Factors of 25: 1, 5, 25
- Common factors:
1
- Greatest:
1
✔ GCF(27, 25) = 1
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✔ Final Answers
| Numbers | Factors | GCF |
|--------|--------|-----|
| 12 → | 1, 2, 3, 4, 6, 12 | |
| 9 → | 1, 3, 9 | GCF(12, 9) =
3 |
| 20 → | 1, 2, 4, 5, 10, 20 | GCF(12, 20) =
4 |
| 30 → | 1, 2, 3, 5, 6, 10, 15, 30 | GCF(12, 30) =
6 |
| 22 → | 1, 2, 11, 22 | GCF(12, 22) =
2 |
| 77 → | 1, 7, 11, 77 | GCF(12, 77) =
1 |
| 27 → | 1, 3, 9, 27 | GCF(27, 25) =
1 |
| 25 → | 1, 5, 25 | |
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📌 Summary of Answers:
- GCF(12, 9) =
3
- GCF(12, 20) =
4
- GCF(12, 30) =
6
- GCF(12, 22) =
2
- GCF(12, 77) =
1
- GCF(27, 25) =
1
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✔ All solved! Let me know if you'd like a printable version or help with more math problems.
Parent Tip: Review the logic above to help your child master the concept of common factors math worksheet.
