Greatest Common Factor (GCF) Practice Problems
Finding and factoring out a GCF is covered fully in the Greatest Common Factor lesson. Since that number-finding step is what every other factoring technique depends on, this practice set isolates and drills it on its own.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | The GCF of two numbers | GCF of |
| Medium | The GCF of three numbers, or a shared variable exponent | GCF of |
| Hard | Bigger numbers, or a negative-GCF’s numeric value | Factoring out |
Easy finds the GCF of two whole numbers directly.
Medium alternates between the GCF of three numbers and the shared exponent of two monomial terms, always the smaller of the two exponents.
Hard alternates between the GCF of three bigger numbers and the numeric value of a negative GCF, factored out so the leading term inside the parentheses becomes positive.
Worked examples
One example at each difficulty level, solved the way the practice set expects.
Easy. Find the GCF of
Medium. Find the GCF of
All three numbers share
Hard. Factor
The GCF of
Using the practice problems
Choose a difficulty and a count, and the practice set produces a new set immediately. Every answer here is a whole number — enter it exactly as computed.
- Check Answers reviews the whole set in one pass and marks the incorrect ones
- Show Answers displays each answer right away, useful for reviewing a worksheet by hand
- Print Worksheet creates a clean page ready to print, ideal for homework or offline practice
The rules these practice problems drill
| Rule | Statement |
|---|---|
| GCF of coefficients | The largest number dividing every coefficient evenly |
| GCF of a repeated variable | The lowest exponent of that variable across every term |
| Negative leading term | Factor out a negative GCF so the term inside becomes positive |
See the Greatest Common Factor lesson for the full technique, including how to factor the GCF out of a complete polynomial.
Common mistakes to watch for
Using the highest exponent instead of the lowest. The GCF of
Stopping at a common factor that isn’t the greatest one.
Dropping the sign when factoring out a negative GCF. Dividing a negative term by a negative GCF gives a positive result — losing track of that sign is the most common error here.
Forgetting a variable missing from even one term. If a variable doesn’t appear in every term, it contributes nothing to the GCF, no matter its exponent elsewhere.
Where to go next
Once spotting a GCF feels automatic, the Factoring by Grouping Practice Problems uses this exact skill twice per problem. For the full technique behind every problem here, see the Greatest Common Factor lesson.