Math worksheet for finding the greatest common factor of number pairs.

Problem Overview:

The task is to find the factors of each given number and then determine the greatest common factor (GCF) for each pair of numbers. The worksheet provides an example to guide the process.

Steps to Solve:

1. Find the Factors of Each Number:
- List all the numbers that divide the given number evenly (i.e., without leaving a remainder).

2. Identify Common Factors:
- Compare the factors of the two numbers in each pair and identify the factors they have in common.

3. Determine the Greatest Common Factor (GCF):
- From the common factors, select the largest one.

Solution:

#### Example Provided:
- Numbers: 12 and 16
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 16: \(1, 2, 4, 8, 16\)
- Common Factors: \(1, 2, 4\)
- GCF: \(4\)

Now, let's solve the problems step by step.

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#### 1. \(12\) and \(9\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 9: \(1, 3, 9\)
- Common Factors: \(1, 3\)
- GCF: \(3\)

#### 2. \(12\) and \(20\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 20: \(1, 2, 4, 5, 10, 20\)
- Common Factors: \(1, 2, 4\)
- GCF: \(4\)

#### 3. \(12\) and \(30\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Common Factors: \(1, 2, 3, 6\)
- GCF: \(6\)

#### 4. \(12\) and \(22\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 22: \(1, 2, 11, 22\)
- Common Factors: \(1, 2\)
- GCF: \(2\)

#### 5. \(12\) and \(77\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Factors of 77: \(1, 7, 11, 77\)
- Common Factors: \(1\)
- GCF: \(1\)

#### 6. \(27\) and \(25\)
- Factors of 27: \(1, 3, 9, 27\)
- Factors of 25: \(1, 5, 25\)
- Common Factors: \(1\)
- GCF: \(1\)

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Final Answers:

\[
\begin{aligned}
&\text{GCF (12, 9)} = 3 \\
&\text{GCF (12, 20)} = 4 \\
&\text{GCF (12, 30)} = 6 \\
&\text{GCF (12, 22)} = 2 \\
&\text{GCF (12, 77)} = 1 \\
&\text{GCF (27, 25)} = 1 \\
\end{aligned}
\]

Boxed Final Answer:

\[
\boxed{3, 4, 6, 2, 1, 1}
\]