Grade 5 Factoring Worksheet: Find the Greatest Common Factor (GCF) of given number pairs.

To solve the problem of finding the greatest common factor (GCF) for each pair of numbers, we will use the method of prime factorization. Here's a step-by-step explanation and solution for each pair:

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Step 1: Understand the GCF

The Greatest Common Factor (GCF) is the largest number that divides both numbers in a pair without leaving a remainder. To find it:
1. Perform prime factorization of each number.
2. Identify the common prime factors.
3. Multiply the common prime factors to get the GCF.

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Step 2: Solve Each Pair

#### Pair 1: 12 and 26
- Prime factorization:
- \( 12 = 2 \times 2 \times 3 \)
- \( 26 = 2 \times 13 \)
- Common prime factors: \( 2 \)
- GCF: \( 2 \)

#### Pair 2: 30 and 40
- Prime factorization:
- \( 30 = 2 \times 3 \times 5 \)
- \( 40 = 2 \times 2 \times 2 \times 5 \)
- Common prime factors: \( 2 \times 5 = 10 \)
- GCF: \( 10 \)

#### Pair 3: 35 and 28
- Prime factorization:
- \( 35 = 5 \times 7 \)
- \( 28 = 2 \times 2 \times 7 \)
- Common prime factors: \( 7 \)
- GCF: \( 7 \)

#### Pair 4: 21 and 15
- Prime factorization:
- \( 21 = 3 \times 7 \)
- \( 15 = 3 \times 5 \)
- Common prime factors: \( 3 \)
- GCF: \( 3 \)

#### Pair 5: 33 and 15
- Prime factorization:
- \( 33 = 3 \times 11 \)
- \( 15 = 3 \times 5 \)
- Common prime factors: \( 3 \)
- GCF: \( 3 \)

#### Pair 6: 27 and 3
- Prime factorization:
- \( 27 = 3 \times 3 \times 3 \)
- \( 3 = 3 \)
- Common prime factors: \( 3 \)
- GCF: \( 3 \)

#### Pair 7: 36 and 33
- Prime factorization:
- \( 36 = 2 \times 2 \times 3 \times 3 \)
- \( 33 = 3 \times 11 \)
- Common prime factors: \( 3 \)
- GCF: \( 3 \)

#### Pair 8: 30 and 5
- Prime factorization:
- \( 30 = 2 \times 3 \times 5 \)
- \( 5 = 5 \)
- Common prime factors: \( 5 \)
- GCF: \( 5 \)

#### Pair 9: 30 and 6
- Prime factorization:
- \( 30 = 2 \times 3 \times 5 \)
- \( 6 = 2 \times 3 \)
- Common prime factors: \( 2 \times 3 = 6 \)
- GCF: \( 6 \)

#### Pair 10: 16 and 4
- Prime factorization:
- \( 16 = 2 \times 2 \times 2 \times 2 \)
- \( 4 = 2 \times 2 \)
- Common prime factors: \( 2 \times 2 = 4 \)
- GCF: \( 4 \)

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Final Answers:

1. \( 12 \) and \( 26 \): \( \boxed{2} \)
2. \( 30 \) and \( 40 \): \( \boxed{10} \)
3. \( 35 \) and \( 28 \): \( \boxed{7} \)
4. \( 21 \) and \( 15 \): \( \boxed{3} \)
5. \( 33 \) and \( 15 \): \( \boxed{3} \)
6. \( 27 \) and \( 3 \): \( \boxed{3} \)
7. \( 36 \) and \( 33 \): \( \boxed{3} \)
8. \( 30 \) and \( 5 \): \( \boxed{5} \)
9. \( 30 \) and \( 6 \): \( \boxed{6} \)
10. \( 16 \) and \( 4 \): \( \boxed{4} \)

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Boxed Final Answer:

\[
\boxed{2, 10, 7, 3, 3, 3, 3, 5, 6, 4}
\]