Grade 5 math worksheet focusing on finding the greatest common factor of given number pairs.

Problem Description:

The task involves finding the Greatest Common Factor (GCF) of given pairs of numbers. The GCF is the largest positive integer that divides both numbers without leaving a remainder.

Solution Approach:

To solve for the GCF of two numbers, we can follow these steps:
1. List the factors of each number: Identify all the positive integers that divide each number evenly.
2. Identify the common factors: Find the factors that are shared by both numbers.
3. Select the greatest common factor: Choose the largest number from the list of common factors.

Let's solve each problem step by step.

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Problem 1: \( 24 \) and \( 36 \)

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

#### Step 2: Identify the common factors
Common factors of \( 24 \) and \( 36 \): \( 1, 2, 3, 4, 6, 12 \)

#### Step 3: Select the greatest common factor
The greatest common factor is \( 12 \).

Answer: \( \boxed{12} \)

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Problem 2: \( 11 \) and \( 27 \)

#### Step 1: List the factors of each number
- Factors of \( 11 \): \( 1, 11 \) (since \( 11 \) is a prime number)
- Factors of \( 27 \): \( 1, 3, 9, 27 \)

#### Step 2: Identify the common factors
Common factors of \( 11 \) and \( 27 \): \( 1 \)

#### Step 3: Select the greatest common factor
The greatest common factor is \( 1 \).

Answer: \( \boxed{1} \)

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Problem 3: \( 15 \) and \( 45 \)

#### Step 1: List the factors of each number
- Factors of \( 15 \): \( 1, 3, 5, 15 \)
- Factors of \( 45 \): \( 1, 3, 5, 9, 15, 45 \)

#### Step 2: Identify the common factors
Common factors of \( 15 \) and \( 45 \): \( 1, 3, 5, 15 \)

#### Step 3: Select the greatest common factor
The greatest common factor is \( 15 \).

Answer: \( \boxed{15} \)

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Problem 4: \( 7 \) and \( 17 \)

#### Step 1: List the factors of each number
- Factors of \( 7 \): \( 1, 7 \) (since \( 7 \) is a prime number)
- Factors of \( 17 \): \( 1, 17 \) (since \( 17 \) is a prime number)

#### Step 2: Identify the common factors
Common factors of \( 7 \) and \( 17 \): \( 1 \)

#### Step 3: Select the greatest common factor
The greatest common factor is \( 1 \).

Answer: \( \boxed{1} \)

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Problem 5: \( 32 \) and \( 48 \)

#### Step 1: List the factors of each number
- Factors of \( 32 \): \( 1, 2, 4, 8, 16, 32 \)
- Factors of \( 48 \): \( 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \)

#### Step 2: Identify the common factors
Common factors of \( 32 \) and \( 48 \): \( 1, 2, 4, 8, 16 \)

#### Step 3: Select the greatest common factor
The greatest common factor is \( 16 \).

Answer: \( \boxed{16} \)

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Final Answers:

1. \( \boxed{12} \)
2. \( \boxed{1} \)
3. \( \boxed{15} \)
4. \( \boxed{1} \)
5. \( \boxed{16} \)

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Summary:

The GCF of two numbers is found by identifying their common factors and selecting the largest one. This method ensures accuracy and works for any pair of integers.