Greatest Common Factor Generator
The Greatest Common Factor lesson covers finding and factoring out a GCF in full; this generator drills the number-finding step directly, since it’s the one skill every other factoring technique depends on getting right first.
How the difficulty levels work
| Difficulty | What it drills | Example |
|---|---|---|
| Easy | The GCF of two numbers | GCF of \(24\) and \(36\) is \(12\) |
| Medium | The GCF of three numbers, or a shared variable exponent | GCF of \(x^{5}\) and \(x^{3}\) has exponent \(3\) |
| Hard | Bigger numbers, or a negative-GCF’s numeric value | Factoring out \(-6x^{2}\) from \(-12x^{3}-18x^{2}\) |
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.
Using the generator
Pick a difficulty and a question count, and a fresh set appears instantly. Every answer here is a whole number — enter it exactly as computed.
- Check Answers scores the set and flags exactly which problems need another look
- Show Answers reveals every solution, useful for reviewing a paper attempt
- Print Worksheet outputs a clean page for offline practice or classroom handouts
The rules this generator drills
| 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 \(x^{2}\) and \(x^{5}\) is \(x^{2}\), not \(x^{5}\) — a higher power doesn’t divide the smaller term.
Stopping at a common factor that isn’t the greatest one. \(2\) is a common factor of \(12\) and \(18\), but \(6\) is 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 Generator uses this exact skill twice per problem. For the full technique behind every problem here, see the Greatest Common Factor lesson.