How to Find the Greatest Common Factor (GCF)? (+FREE Worksheet!)
Find the Greatest Common Factor (GCF): what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Organize by degreeWrite terms from highest power to lowest power.
- Look for structureTry GCF, special products, grouping, or division depending on the expression.
- Check with featuresZeros, multiplicity, and end behavior should agree with your algebra.
Worked examples
Combine like terms
- Group x squared terms.
- Group x terms.
- Combine each group.
Factor a difference of squares
- Recognize a squared term minus a squared term.
- Use a^2 – b^2.
- Write conjugate factors.
Try one before moving on
Find the Greatest Common Factor (GCF): pop-up practice
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: \( \{1,2,3,4,6,12\} \)
Numbers \(2\) and \(4\) are in common.
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: \(2\).
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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 \(25\) 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.
- \(\color{blue}{20, 30}\)
- \(\color{blue}{4, 14}\)
- \(\color{blue}{5, 45}\)
- \(\color{blue}{68, 12}\)
- \(\color{blue}{5, 6, 12}\)
- \(\color{blue}{15, 27, 33}\)
Download Greatest Common Factor Worksheet
- \(\color{blue}{10}\)
- \(\color{blue}{2}\)
- \(\color{blue}{5}\)
- \(\color{blue}{4}\)
- \(\color{blue}{1}\)
- \(\color{blue}{3}\)
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Watch this practice video for additional examples and reinforcement:
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