Greatest Common Factor

In this post, you learn how to find Greatest Common Factor of two or more numbers.

Step by step guide to finding Greatest Common Factor

• List the prime factors of each number.
• Multiply common prime factors.
• If there are no common prime factors, the GCF (Greatest Common Factor) is \(1\).

Example 1:

Find the GCF for \(8\) and \(12\).

Solution:

The factors of \(8\) are: \( \{1, 2, 4, 8\} \)
The factors of \(12\) are: \( \{1,2,3,4,6,12\} \)
Number \(4\) is in both factors.
Then the greatest common factor is: \(4\).

Example 2:

Find the GCF for \(14\) and \(18\).

Solution:

The factors of \(14\) are: \( \{1,2,7,14\} \)
The factors of \(18\) are: \( \{1,2,3,6,9,18\} \)
There is \(2\) in common
Then the greatest common factor is: \(2\).

Example 3:

Find the GCF for \(10\) and \(15\) and \(25\) .

Solution:

The factors of \(10\) are: \(\{1,2,5,10\}\)
The factors of \(15\) are: \(\{1,3,5,15\}\)
The factors of \(12\) are: \(\{1,5,25\}\)
Factor \(5\) is in common.
Then the greatest common factor is: \(5\).

Example 4:

Find the GCF for \(8\) and \(20\).

Solution:

The factors of \(8\) are: \(\{1,2,4,8\}\)
The factors of \(20\) are: \(\{1,2,4,5,10,20\}\)
Numbers \(2\) and \(4\) are in common.
Then the greatest common factor is: \(4\).

Exercises

Find the GCF for each number pair.

1. \(\color{blue}{20, 30}\)
2. \(\color{blue}{4, 14}\)
3. \(\color{blue}{5, 45}\)
4. \(\color{blue}{68, 12}\)
5. \(\color{blue}{5, 6, 12}\)
6. \(\color{blue}{15, 27, 33}\)

Download Greatest Common Factor Worksheet

1. \(\color{blue}{10}\)
2. \(\color{blue}{2}\)
3. \(\color{blue}{5}\)
4. \(\color{blue}{4}\)
5. \(\color{blue}{1}\)
6. \(\color{blue}{3}\)