How to Find the Greatest Common Factor (GCF)? (+FREE Worksheet!)
How to find the greatest common factor (GCF), step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.
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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