How to Find the Greatest Common Factor (GCF)

How to Find the Greatest Common Factor (GCF)

In this post, you learn how to find the Greatest Common Factor (GCF) of two or more numbers using a few simple and easy steps.

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Step by step guide to finding the 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 \(1\).

Greatest Common Factor – 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: \(4\).

Greatest Common Factor – 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: \(2\).

Greatest Common Factor – 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: \(5\).

Greatest Common Factor – 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 for practicing the Greatest Common Factor

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. \(\color{blue}{3}\)

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  1. Savannah says:

    The greatest common factor for 8 and 20 is 4. The text multiplies 2 and 4 to find 8 but since 8 does not factor into 20 that cannot be correct.

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