Greatest Common Factor practice worksheet with 24 problems for finding GCF of number pairs.

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.

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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

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2) GCF(12, 15)

- 12: 1, 2, 3, 4, 6, 12
- 15: 1, 3, 5, 15
- Common: 1, 3 → GCF = 3

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3) GCF(13, 18)

- 13 is prime → factors: 1, 13
- 18: 1, 2, 3, 6, 9, 18
- Only common factor: 1 → GCF = 1

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4) GCF(22, 16)

- 22: 1, 2, 11, 22
- 16: 1, 2, 4, 8, 16
- Common: 1, 2 → GCF = 2

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5) GCF(24, 15)

- 24: 1, 2, 3, 4, 6, 8, 12, 24
- 15: 1, 3, 5, 15
- Common: 1, 3 → GCF = 3

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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

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7) GCF(21, 32)

- 21: 1, 3, 7, 21
- 32: 1, 2, 4, 8, 16, 32
- Only common: 1 → GCF = 1

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8) GCF(18, 27)

- 18: 1, 2, 3, 6, 9, 18
- 27: 1, 3, 9, 27
- Common: 1, 3, 9 → GCF = 9

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9) GCF(33, 25)

- 33: 1, 3, 11, 33
- 25: 1, 5, 25
- Only common: 1 → GCF = 1

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10) GCF(28, 21)

- 28: 1, 2, 4, 7, 14, 28
- 21: 1, 3, 7, 21
- Common: 1, 7 → GCF = 7

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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

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12) GCF(32, 12)

- 32: 1, 2, 4, 8, 16, 32
- 12: 1, 2, 3, 4, 6, 12
- Common: 1, 2, 4 → GCF = 4

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13) GCF(25, 45)

- 25: 1, 5, 25
- 45: 1, 3, 5, 9, 15, 45
- Common: 1, 5 → GCF = 5

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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

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15) GCF(36, 21)

- 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
- 21: 1, 3, 7, 21
- Common: 1, 3 → GCF = 3

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16) GCF(22, 33)

- 22: 1, 2, 11, 22
- 33: 1, 3, 11, 33
- Common: 1, 11 → GCF = 11

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17) GCF(21, 16)

- 21: 1, 3, 7, 21
- 16: 1, 2, 4, 8, 16
- Only common: 1 → GCF = 1

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18) GCF(35, 28)

- 35: 1, 5, 7, 35
- 28: 1, 2, 4, 7, 14, 28
- Common: 1, 7 → GCF = 7

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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

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20) GCF(26, 34)

- 26: 1, 2, 13, 26
- 34: 1, 2, 17, 34
- Common: 1, 2 → GCF = 2

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21) GCF(31, 23)

- Both are prime numbers
- Only common factor: 1 → GCF = 1

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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

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23) GCF(26, 38)

- 26: 1, 2, 13, 26
- 38: 1, 2, 19, 38
- Common: 1, 2 → GCF = 2

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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

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✔ Final Answers:

| # | GCF |
|---|-----|
| 1 | 2 |
| 2 | 3 |
| 3 | 1 |
| 4 | 2 |
| 5 | 3 |
| 6 | 6 |
| 7 | 1 |
| 8 | 9 |
| 9 | 1 |
|10 | 7 |
|11 | 8 |
|12 | 4 |
|13 | 5 |
|14 | 18 |
|15 | 3 |
|16 | 11 |
|17 | 1 |
|18 | 7 |
|19 | 6 |
|20 | 2 |
|21 | 1 |
|22 | 4 |
|23 | 2 |
|24 | 21 |

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