Printable math worksheet for practicing finding the greatest common factor of number pairs.

To solve the problem of finding the greatest common factor (GCF) for each pair of numbers, we need to follow these steps:

1. List the factors of each number in the pair.
2. Identify the common factors between the two numbers.
3. Determine the greatest common factor from the list of common factors.

Let's solve each pair step by step.

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Pair 1: 8 and 12

#### Step 1: List the factors of each number.
- Factors of 8: \(1, 2, 4, 8\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)

#### Step 2: Identify the common factors.
- Common factors of 8 and 12: \(1, 2, 4\)

#### Step 3: Determine the greatest common factor.
- The greatest common factor is \(4\).

Answer for 8 and 12:
- Factors of 8: \(1, 2, 4, 8\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Greatest Common Factor: \(4\)

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Pair 2: 18 and 24

#### Step 1: List the factors of each number.
- Factors of 18: \(1, 2, 3, 6, 9, 18\)
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)

#### Step 2: Identify the common factors.
- Common factors of 18 and 24: \(1, 2, 3, 6\)

#### Step 3: Determine the greatest common factor.
- The greatest common factor is \(6\).

Answer for 18 and 24:
- Factors of 18: \(1, 2, 3, 6, 9, 18\)
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
- Greatest Common Factor: \(6\)

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Pair 3: 35 and 42

#### Step 1: List the factors of each number.
- Factors of 35: \(1, 5, 7, 35\)
- Factors of 42: \(1, 2, 3, 6, 7, 14, 21, 42\)

#### Step 2: Identify the common factors.
- Common factors of 35 and 42: \(1, 7\)

#### Step 3: Determine the greatest common factor.
- The greatest common factor is \(7\).

Answer for 35 and 42:
- Factors of 35: \(1, 5, 7, 35\)
- Factors of 42: \(1, 2, 3, 6, 7, 14, 21, 42\)
- Greatest Common Factor: \(7\)

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Pair 4: 72 and 48

#### Step 1: List the factors of each number.
- Factors of 72: \(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\)
- Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)

#### Step 2: Identify the common factors.
- Common factors of 72 and 48: \(1, 2, 3, 4, 6, 8, 12, 24\)

#### Step 3: Determine the greatest common factor.
- The greatest common factor is \(24\).

Answer for 72 and 48:
- Factors of 72: \(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\)
- Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)
- Greatest Common Factor: \(24\)

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Pair 5: 33 and 55

#### Step 1: List the factors of each number.
- Factors of 33: \(1, 3, 11, 33\)
- Factors of 55: \(1, 5, 11, 55\)

#### Step 2: Identify the common factors.
- Common factors of 33 and 55: \(1, 11\)

#### Step 3: Determine the greatest common factor.
- The greatest common factor is \(11\).

Answer for 33 and 55:
- Factors of 33: \(1, 3, 11, 33\)
- Factors of 55: \(1, 5, 11, 55\)
- Greatest Common Factor: \(11\)

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Final Answers:

1. 8 and 12:
- Factors of 8: \(1, 2, 4, 8\)
- Factors of 12: \(1, 2, 3, 4, 6, 12\)
- Greatest Common Factor: \(\boxed{4}\)

2. 18 and 24:
- Factors of 18: \(1, 2, 3, 6, 9, 18\)
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)
- Greatest Common Factor: \(\boxed{6}\)

3. 35 and 42:
- Factors of 35: \(1, 5, 7, 35\)
- Factors of 42: \(1, 2, 3, 6, 7, 14, 21, 42\)
- Greatest Common Factor: \(\boxed{7}\)

4. 72 and 48:
- Factors of 72: \(1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\)
- Factors of 48: \(1, 2, 3, 4, 6, 8, 12, 16, 24, 48\)
- Greatest Common Factor: \(\boxed{24}\)

5. 33 and 55:
- Factors of 33: \(1, 3, 11, 33\)
- Factors of 55: \(1, 5, 11, 55\)
- Greatest Common Factor: \(\boxed{11}\)

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Boxed Final Answers:

\[
\boxed{4, 6, 7, 24, 11}
\]