Greatest Common Factor GCF Worksheets - Free Printable

Problem Overview:

The task is to find the Greatest Common Factor (GCF) for each pair of numbers using the ladder method. The worksheet provides an example of how to use the ladder method to identify the GCF and LCM of two numbers.

Ladder Method Recap:

1. Write the two numbers on one line.
2. Draw a "ladder" shape.
3. Divide out common prime numbers starting with the smallest.
4. The GCF is the product of the numbers on the left side of the ladder (in green in the example).

Step-by-Step Solution:

#### Pair (i): (20, 14)
1. Write the numbers: 20 and 14.
2. Start dividing by the smallest common prime factor:
- Both 20 and 14 are divisible by 2.
\[
20 \div 2 = 10, \quad 14 \div 2 = 7
\]
- Now we have 10 and 7. These numbers have no common factors other than 1.
3. The GCF is the product of the numbers on the left side of the ladder, which is \(2\).

Answer: \(\boxed{2}\)

#### Pair (ii): (5, 35)
1. Write the numbers: 5 and 35.
2. Start dividing by the smallest common prime factor:
- Both 5 and 35 are divisible by 5.
\[
5 \div 5 = 1, \quad 35 \div 5 = 7
\]
- Now we have 1 and 7. These numbers have no common factors other than 1.
3. The GCF is the product of the numbers on the left side of the ladder, which is \(5\).

Answer: \(\boxed{5}\)

#### Pair (iii): (39, 12)
1. Write the numbers: 39 and 12.
2. Start dividing by the smallest common prime factor:
- Both 39 and 12 are divisible by 3.
\[
39 \div 3 = 13, \quad 12 \div 3 = 4
\]
- Now we have 13 and 4. These numbers have no common factors other than 1.
3. The GCF is the product of the numbers on the left side of the ladder, which is \(3\).

Answer: \(\boxed{3}\)

#### Pair (iv): (14, 34)
1. Write the numbers: 14 and 34.
2. Start dividing by the smallest common prime factor:
- Both 14 and 34 are divisible by 2.
\[
14 \div 2 = 7, \quad 34 \div 2 = 17
\]
- Now we have 7 and 17. These numbers have no common factors other than 1.
3. The GCF is the product of the numbers on the left side of the ladder, which is \(2\).

Answer: \(\boxed{2}\)

#### Pair (v): (30, 24)
1. Write the numbers: 30 and 24.
2. Start dividing by the smallest common prime factor:
- Both 30 and 24 are divisible by 2.
\[
30 \div 2 = 15, \quad 24 \div 2 = 12
\]
- Both 15 and 12 are divisible by 3.
\[
15 \div 3 = 5, \quad 12 \div 3 = 4
\]
- Now we have 5 and 4. These numbers have no common factors other than 1.
3. The GCF is the product of the numbers on the left side of the ladder, which is \(2 \times 3 = 6\).

Answer: \(\boxed{6}\)

#### Pair (vi): (40, 5)
1. Write the numbers: 40 and 5.
2. Start dividing by the smallest common prime factor:
- Both 40 and 5 are divisible by 5.
\[
40 \div 5 = 8, \quad 5 \div 5 = 1
\]
- Now we have 8 and 1. These numbers have no common factors other than 1.
3. The GCF is the product of the numbers on the left side of the ladder, which is \(5\).

Answer: \(\boxed{5}\)

Final Answers:

\[
\boxed{2, 5, 3, 2, 6, 5}
\]