Grade 5 Factoring Worksheets: Greatest Common Factor of two ... - Free Printable

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:

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