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 part step by step.

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Part a: 30 and 10

#### Step 1: List the factors of each number.
- Factors of 30: \(1, 2, 3, 5, 6, 10, 15, 30\)
- Factors of 10: \(1, 2, 5, 10\)

#### Step 2: Identify the common factors.
The common factors of 30 and 10 are: \(1, 2, 5, 10\).

#### Step 3: Determine the greatest common factor.
The greatest common factor is \(10\).

Answer for Part a: \(\boxed{10}\)

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Part b: 78 and 26

#### Step 1: List the factors of each number.
- Factors of 78: \(1, 2, 3, 6, 13, 26, 39, 78\)
- Factors of 26: \(1, 2, 13, 26\)

#### Step 2: Identify the common factors.
The common factors of 78 and 26 are: \(1, 2, 13, 26\).

#### Step 3: Determine the greatest common factor.
The greatest common factor is \(26\).

Answer for Part b: \(\boxed{26}\)

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Part c: 60 and 68

#### Step 1: List the factors of each number.
- Factors of 60: \(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60\)
- Factors of 68: \(1, 2, 4, 17, 34, 68\)

#### Step 2: Identify the common factors.
The common factors of 60 and 68 are: \(1, 2, 4\).

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

Answer for Part c: \(\boxed{4}\)

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Part d: 70 and 20

#### Step 1: List the factors of each number.
- Factors of 70: \(1, 2, 5, 7, 10, 14, 35, 70\)
- Factors of 20: \(1, 2, 4, 5, 10, 20\)

#### Step 2: Identify the common factors.
The common factors of 70 and 20 are: \(1, 2, 5, 10\).

#### Step 3: Determine the greatest common factor.
The greatest common factor is \(10\).

Answer for Part d: \(\boxed{10}\)

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Part e: 40 and 24

#### Step 1: List the factors of each number.
- Factors of 40: \(1, 2, 4, 5, 8, 10, 20, 40\)
- Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)

#### Step 2: Identify the common factors.
The common factors of 40 and 24 are: \(1, 2, 4, 8\).

#### Step 3: Determine the greatest common factor.
The greatest common factor is \(8\).

Answer for Part e: \(\boxed{8}\)

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Final Answers:

\[
\boxed{10, 26, 4, 10, 8}
\]