Printable math worksheet for finding the greatest common factor of three numbers.

To solve the problem of finding the Greatest Common Factor (GCF) of each set of numbers, we will use the method of prime factorization. The GCF is the product of the lowest powers of all common prime factors in the given numbers.

Step-by-Step Solution:

#### 1) GCF(8, 14, 12)
- Prime factorization:
- \( 8 = 2^3 \)
- \( 14 = 2 \times 7 \)
- \( 12 = 2^2 \times 3 \)
- Common prime factors: The only common prime factor is \( 2 \).
- Lowest power of common factors: \( 2^1 = 2 \)
- GCF: \( 2 \)

#### 2) GCF(12, 24, 14)
- Prime factorization:
- \( 12 = 2^2 \times 3 \)
- \( 24 = 2^3 \times 3 \)
- \( 14 = 2 \times 7 \)
- Common prime factors: The only common prime factor is \( 2 \).
- Lowest power of common factors: \( 2^1 = 2 \)
- GCF: \( 2 \)

#### 3) GCF(15, 20, 5)
- Prime factorization:
- \( 15 = 3 \times 5 \)
- \( 20 = 2^2 \times 5 \)
- \( 5 = 5 \)
- Common prime factors: The only common prime factor is \( 5 \).
- Lowest power of common factors: \( 5^1 = 5 \)
- GCF: \( 5 \)

#### 4) GCF(4, 16, 6)
- Prime factorization:
- \( 4 = 2^2 \)
- \( 16 = 2^4 \)
- \( 6 = 2 \times 3 \)
- Common prime factors: The only common prime factor is \( 2 \).
- Lowest power of common factors: \( 2^1 = 2 \)
- GCF: \( 2 \)

#### 5) GCF(24, 15, 6)
- Prime factorization:
- \( 24 = 2^3 \times 3 \)
- \( 15 = 3 \times 5 \)
- \( 6 = 2 \times 3 \)
- Common prime factors: The only common prime factor is \( 3 \).
- Lowest power of common factors: \( 3^1 = 3 \)
- GCF: \( 3 \)

#### 6) GCF(7, 21, 18)
- Prime factorization:
- \( 7 = 7 \)
- \( 21 = 3 \times 7 \)
- \( 18 = 2 \times 3^2 \)
- Common prime factors: There are no common prime factors.
- GCF: \( 1 \)

#### 7) GCF(12, 2, 24)
- Prime factorization:
- \( 12 = 2^2 \times 3 \)
- \( 2 = 2 \)
- \( 24 = 2^3 \times 3 \)
- Common prime factors: The only common prime factor is \( 2 \).
- Lowest power of common factors: \( 2^1 = 2 \)
- GCF: \( 2 \)

#### 8) GCF(20, 10, 25)
- Prime factorization:
- \( 20 = 2^2 \times 5 \)
- \( 10 = 2 \times 5 \)
- \( 25 = 5^2 \)
- Common prime factors: The only common prime factor is \( 5 \).
- Lowest power of common factors: \( 5^1 = 5 \)
- GCF: \( 5 \)

#### 9) GCF(3, 18, 9)
- Prime factorization:
- \( 3 = 3 \)
- \( 18 = 2 \times 3^2 \)
- \( 9 = 3^2 \)
- Common prime factors: The only common prime factor is \( 3 \).
- Lowest power of common factors: \( 3^1 = 3 \)
- GCF: \( 3 \)

#### 10) GCF(6, 16, 18)
- Prime factorization:
- \( 6 = 2 \times 3 \)
- \( 16 = 2^4 \)
- \( 18 = 2 \times 3^2 \)
- Common prime factors: The only common prime factor is \( 2 \).
- Lowest power of common factors: \( 2^1 = 2 \)
- GCF: \( 2 \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1) & 2 \\
2) & 2 \\
3) & 5 \\
4) & 2 \\
5) & 3 \\
6) & 1 \\
7) & 2 \\
8) & 5 \\
9) & 3 \\
10) & 2 \\
\end{array}
}
\]