Calculator Form
Enter terms on separate lines, with commas, or as one expression.
Example Data Table
These sample rows show how the calculator interprets common factoring patterns.
| Expression terms | Numeric GCF | Variable GCF | Final factored form |
|---|---|---|---|
| 12x^3y, 18x^2y^2, 24x^2y | 6 | x^2y | 6x^2y(2x + 3y + 4) |
| 14a^2b, 21ab^3, 35ab | 7 | ab | 7ab(2a + 3b^2 + 5) |
| -8m^3n, 12m^2n^2, -20mn | 4 | mn | 4mn(-2m^2 + 3mn - 5) |
Formula Used
Numeric part: GCF of coefficients = gcd(|a₁|, |a₂|, ..., |aₙ|)
Variable part: For each shared variable, keep the smallest exponent across all terms.
Final factorization: Expression = GCF × (each term divided by that GCF)
For monomials, the greatest common factor combines two pieces. First, the calculator finds the greatest common divisor of all absolute coefficients. Second, it checks every variable appearing in all terms and keeps that variable with the minimum exponent found.
After that, every original term is divided by the shared factor. The quotient terms stay inside parentheses, giving the final factored expression.
How to Use This Calculator
- Enter two or more monomial terms in the input box. Use commas, line breaks, or a full expression with plus and minus signs.
- Write exponents with the caret symbol, such as x^3 or a^2b.
- Choose a graph style and decide whether to show prime factors and the reduction table.
- Press Factor by GCF to place the result above the form.
- Review the GCF, reduced terms, step breakdown, and graph.
- Use the CSV or PDF buttons to export your result summary.
Frequently Asked Questions
1. What does GCF factoring mean?
It means pulling out the greatest common factor shared by every term. The remaining pieces stay inside parentheses as a simpler expression.
2. Can I enter constants with variables?
Yes. A term may be a constant, a variable term, or both. Constants simply have no variable part.
3. Why are absolute coefficients used for the GCF?
The greatest common factor is usually taken as positive. Signs remain with the reduced terms inside the parentheses.
4. What happens if no variable is shared?
The calculator still factors out the numeric GCF if one exists. If nothing greater than one is shared, the expression stays essentially unchanged.
5. Can this handle full polynomials?
It handles polynomials made of monomial terms. Each term should be simple, like 12x^2y or -9ab^3.
6. Does order matter when entering variables?
No. The calculator normalizes variables internally and displays them in a consistent alphabetical order for clarity.
7. Why is the reduced term sometimes just a number?
That happens when the entire variable part was included in the GCF. After division, only the leftover numeric coefficient remains.
8. What do the export buttons save?
CSV saves the reduction table. PDF saves a text summary of the result section, including the main factoring outcome and steps.