Greatest Common Factor Worksheet page - Free Printable
Educational worksheet: Greatest Common Factor Worksheet page. Download and print for classroom or home learning activities.
GIF
1000×1294
57 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #1186126
⭐
Show Answer Key & Explanations
Step-by-step solution for: Greatest Common Factor Worksheet page
▼
Show Answer Key & Explanations
Step-by-step solution for: Greatest Common Factor Worksheet page
Let's solve each of these Greatest Common Factor (GCF) problems step by step. The GCF of two numbers is the largest positive integer that divides both numbers without leaving a remainder.
We'll use prime factorization or listing factors to find the GCF for each pair.
---
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 14: 1, 2, 7, 14
- Common factors: 1, 2 → GCF = 2
---
- 12: 1, 2, 3, 4, 6, 12
- 15: 1, 3, 5, 15
- Common: 1, 3 → GCF = 3
---
- 13 is prime → factors: 1, 13
- 18: 1, 2, 3, 6, 9, 18
- Only common factor: 1 → GCF = 1
---
- 22: 1, 2, 11, 22
- 16: 1, 2, 4, 8, 16
- Common: 1, 2 → GCF = 2
---
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- 15: 1, 3, 5, 15
- Common: 1, 3 → GCF = 3
---
- 18: 1, 2, 3, 6, 9, 18
- 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common: 1, 2, 3, 6 → GCF = 6
---
- 21: 1, 3, 7, 21
- 32: 1, 2, 4, 8, 16, 32
- Only common: 1 → GCF = 1
---
- 18: 1, 2, 3, 6, 9, 18
- 27: 1, 3, 9, 27
- Common: 1, 3, 9 → GCF = 9
---
- 33: 1, 3, 11, 33
- 25: 1, 5, 25
- Only common: 1 → GCF = 1
---
- 28: 1, 2, 4, 7, 14, 28
- 21: 1, 3, 7, 21
- Common: 1, 7 → GCF = 7
---
- 16: 1, 2, 4, 8, 16
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common: 1, 2, 4, 8 → GCF = 8
---
- 32: 1, 2, 4, 8, 16, 32
- 12: 1, 2, 3, 4, 6, 12
- Common: 1, 2, 4 → GCF = 4
---
- 25: 1, 5, 25
- 45: 1, 3, 5, 9, 15, 45
- Common: 1, 5 → GCF = 5
---
- 18: 1, 2, 3, 6, 9, 18
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Common: 1, 2, 3, 6, 9, 18 → GCF = 18
---
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- 21: 1, 3, 7, 21
- Common: 1, 3 → GCF = 3
---
- 22: 1, 2, 11, 22
- 33: 1, 3, 11, 33
- Common: 1, 11 → GCF = 11
---
- 21: 1, 3, 7, 21
- 16: 1, 2, 4, 8, 16
- Only common: 1 → GCF = 1
---
- 35: 1, 5, 7, 35
- 28: 1, 2, 4, 7, 14, 28
- Common: 1, 7 → GCF = 7
---
- 30: 1, 2, 3, 5, 6, 10, 15, 30
- 42: 1, 2, 3, 6, 7, 14, 21, 42
- Common: 1, 2, 3, 6 → GCF = 6
---
- 26: 1, 2, 13, 26
- 34: 1, 2, 17, 34
- Common: 1, 2 → GCF = 2
---
- Both are prime numbers
- Only common factor: 1 → GCF = 1
---
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- 44: 1, 2, 4, 11, 22, 44
- Common: 1, 2, 4 → GCF = 4
---
- 26: 1, 2, 13, 26
- 38: 1, 2, 19, 38
- Common: 1, 2 → GCF = 2
---
- 42: 1, 2, 3, 6, 7, 14, 21, 42
- 21: 1, 3, 7, 21
- Common: 1, 3, 7, 21 → GCF = 21
---
| Problem | Answer |
|--------|--------|
| 1) GCF(20,14) | 2 |
| 2) GCF(12,15) | 3 |
| 3) GCF(13,18) | 1 |
| 4) GCF(22,16) | 2 |
| 5) GCF(24,15) | 3 |
| 6) GCF(18,30) | 6 |
| 7) GCF(21,32) | 1 |
| 8) GCF(18,27) | 9 |
| 9) GCF(33,25) | 1 |
| 10) GCF(28,21) | 7 |
| 11) GCF(16,24) | 8 |
| 12) GCF(32,12) | 4 |
| 13) GCF(25,45) | 5 |
| 14) GCF(18,36) | 18 |
| 15) GCF(36,21) | 3 |
| 16) GCF(22,33) | 11 |
| 17) GCF(21,16) | 1 |
| 18) GCF(35,28) | 7 |
| 19) GCF(30,42) | 6 |
| 20) GCF(26,34) | 2 |
| 21) GCF(31,23) | 1 |
| 22) GCF(36,44) | 4 |
| 23) GCF(26,38) | 2 |
| 24) GCF(42,21) | 21 |
---
✔ Summary Tips:
- If one number divides the other exactly, the smaller number is the GCF.
- If two numbers are prime or coprime (no common factors except 1), GCF = 1.
- Use prime factorization for larger numbers.
Let me know if you'd like this in printable format or with explanations using prime factorization!
We'll use prime factorization or listing factors to find the GCF for each pair.
---
1) GCF(20, 14)
- Factors of 20: 1, 2, 4, 5, 10, 20
- Factors of 14: 1, 2, 7, 14
- Common factors: 1, 2 → GCF = 2
---
2) GCF(12, 15)
- 12: 1, 2, 3, 4, 6, 12
- 15: 1, 3, 5, 15
- Common: 1, 3 → GCF = 3
---
3) GCF(13, 18)
- 13 is prime → factors: 1, 13
- 18: 1, 2, 3, 6, 9, 18
- Only common factor: 1 → GCF = 1
---
4) GCF(22, 16)
- 22: 1, 2, 11, 22
- 16: 1, 2, 4, 8, 16
- Common: 1, 2 → GCF = 2
---
5) GCF(24, 15)
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- 15: 1, 3, 5, 15
- Common: 1, 3 → GCF = 3
---
6) GCF(18, 30)
- 18: 1, 2, 3, 6, 9, 18
- 30: 1, 2, 3, 5, 6, 10, 15, 30
- Common: 1, 2, 3, 6 → GCF = 6
---
7) GCF(21, 32)
- 21: 1, 3, 7, 21
- 32: 1, 2, 4, 8, 16, 32
- Only common: 1 → GCF = 1
---
8) GCF(18, 27)
- 18: 1, 2, 3, 6, 9, 18
- 27: 1, 3, 9, 27
- Common: 1, 3, 9 → GCF = 9
---
9) GCF(33, 25)
- 33: 1, 3, 11, 33
- 25: 1, 5, 25
- Only common: 1 → GCF = 1
---
10) GCF(28, 21)
- 28: 1, 2, 4, 7, 14, 28
- 21: 1, 3, 7, 21
- Common: 1, 7 → GCF = 7
---
11) GCF(16, 24)
- 16: 1, 2, 4, 8, 16
- 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common: 1, 2, 4, 8 → GCF = 8
---
12) GCF(32, 12)
- 32: 1, 2, 4, 8, 16, 32
- 12: 1, 2, 3, 4, 6, 12
- Common: 1, 2, 4 → GCF = 4
---
13) GCF(25, 45)
- 25: 1, 5, 25
- 45: 1, 3, 5, 9, 15, 45
- Common: 1, 5 → GCF = 5
---
14) GCF(18, 36)
- 18: 1, 2, 3, 6, 9, 18
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- Common: 1, 2, 3, 6, 9, 18 → GCF = 18
---
15) GCF(36, 21)
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- 21: 1, 3, 7, 21
- Common: 1, 3 → GCF = 3
---
16) GCF(22, 33)
- 22: 1, 2, 11, 22
- 33: 1, 3, 11, 33
- Common: 1, 11 → GCF = 11
---
17) GCF(21, 16)
- 21: 1, 3, 7, 21
- 16: 1, 2, 4, 8, 16
- Only common: 1 → GCF = 1
---
18) GCF(35, 28)
- 35: 1, 5, 7, 35
- 28: 1, 2, 4, 7, 14, 28
- Common: 1, 7 → GCF = 7
---
19) GCF(30, 42)
- 30: 1, 2, 3, 5, 6, 10, 15, 30
- 42: 1, 2, 3, 6, 7, 14, 21, 42
- Common: 1, 2, 3, 6 → GCF = 6
---
20) GCF(26, 34)
- 26: 1, 2, 13, 26
- 34: 1, 2, 17, 34
- Common: 1, 2 → GCF = 2
---
21) GCF(31, 23)
- Both are prime numbers
- Only common factor: 1 → GCF = 1
---
22) GCF(36, 44)
- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- 44: 1, 2, 4, 11, 22, 44
- Common: 1, 2, 4 → GCF = 4
---
23) GCF(26, 38)
- 26: 1, 2, 13, 26
- 38: 1, 2, 19, 38
- Common: 1, 2 → GCF = 2
---
24) GCF(42, 21)
- 42: 1, 2, 3, 6, 7, 14, 21, 42
- 21: 1, 3, 7, 21
- Common: 1, 3, 7, 21 → GCF = 21
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1) GCF(20,14) | 2 |
| 2) GCF(12,15) | 3 |
| 3) GCF(13,18) | 1 |
| 4) GCF(22,16) | 2 |
| 5) GCF(24,15) | 3 |
| 6) GCF(18,30) | 6 |
| 7) GCF(21,32) | 1 |
| 8) GCF(18,27) | 9 |
| 9) GCF(33,25) | 1 |
| 10) GCF(28,21) | 7 |
| 11) GCF(16,24) | 8 |
| 12) GCF(32,12) | 4 |
| 13) GCF(25,45) | 5 |
| 14) GCF(18,36) | 18 |
| 15) GCF(36,21) | 3 |
| 16) GCF(22,33) | 11 |
| 17) GCF(21,16) | 1 |
| 18) GCF(35,28) | 7 |
| 19) GCF(30,42) | 6 |
| 20) GCF(26,34) | 2 |
| 21) GCF(31,23) | 1 |
| 22) GCF(36,44) | 4 |
| 23) GCF(26,38) | 2 |
| 24) GCF(42,21) | 21 |
---
✔ Summary Tips:
- If one number divides the other exactly, the smaller number is the GCF.
- If two numbers are prime or coprime (no common factors except 1), GCF = 1.
- Use prime factorization for larger numbers.
Let me know if you'd like this in printable format or with explanations using prime factorization!
Parent Tip: Review the logic above to help your child master the concept of greatest common factor worksheet printable.
