Printable math worksheet for finding the greatest common factor using prime factorization.

To solve the problem of finding the Greatest Common Factor (GCF) for each pair of numbers, we need to follow these steps:

Step-by-Step Solution:

#### 1. Pair: 18 and 12
- Prime factorization:
- \( 18 = 2 \times 3 \times 3 \)
- \( 12 = 2 \times 2 \times 3 \)
- Common prime factors: \( 2 \) and \( 3 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 2^1 \times 3^1 = 6 \)
- Answer: GCF = 6

#### 2. Pair: 20 and 30
- Prime factorization:
- \( 20 = 2 \times 2 \times 5 \)
- \( 30 = 2 \times 3 \times 5 \)
- Common prime factors: \( 2 \) and \( 5 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 2^1 \times 5^1 = 10 \)
- Answer: GCF = 10

#### 3. Pair: 6 and 10
- Prime factorization:
- \( 6 = 2 \times 3 \)
- \( 10 = 2 \times 5 \)
- Common prime factors: \( 2 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 2^1 = 2 \)
- Answer: GCF = 2

#### 4. Pair: 25 and 50
- Prime factorization:
- \( 25 = 5 \times 5 \)
- \( 50 = 2 \times 5 \times 5 \)
- Common prime factors: \( 5 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 5^2 = 25 \)
- Answer: GCF = 25

#### 5. Pair: 15 and 45
- Prime factorization:
- \( 15 = 3 \times 5 \)
- \( 45 = 3 \times 3 \times 5 \)
- Common prime factors: \( 3 \) and \( 5 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 3^1 \times 5^1 = 15 \)
- Answer: GCF = 15

#### 6. Pair: 14 and 35
- Prime factorization:
- \( 14 = 2 \times 7 \)
- \( 35 = 5 \times 7 \)
- Common prime factors: \( 7 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 7^1 = 7 \)
- Answer: GCF = 7

#### 7. Pair: 30 and 45
- Prime factorization:
- \( 30 = 2 \times 3 \times 5 \)
- \( 45 = 3 \times 3 \times 5 \)
- Common prime factors: \( 3 \) and \( 5 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 3^1 \times 5^1 = 15 \)
- Answer: GCF = 15

#### 8. Pair: 24 and 36
- Prime factorization:
- \( 24 = 2 \times 2 \times 2 \times 3 \)
- \( 36 = 2 \times 2 \times 3 \times 3 \)
- Common prime factors: \( 2 \) and \( 3 \)
- GCF: Multiply the common prime factors with the lowest powers.
- \( 2^2 \times 3^1 = 4 \times 3 = 12 \)
- Answer: GCF = 12

Final Answers:

1. GCF = 6
2. GCF = 10
3. GCF = 2
4. GCF = 25
5. GCF = 15
6. GCF = 7
7. GCF = 15
8. GCF = 12

Boxed Final Answer:

\[
\boxed{6, 10, 2, 25, 15, 7, 15, 12}
\]