Calculator Form
Example Data Table
| Example | Monomials | Coefficient GCD | Shared Variable Exponents | Monomial GCF |
|---|---|---|---|---|
| 1 | 12x^3y^2, 18x^2y^5, 30x^4y | 6 | x^2, y^1 | 6x^2y |
| 2 | 14a^4b^2, 21a^2b^5, 35a^3b | 7 | a^2, b^1 | 7a^2b |
| 3 | 8m^3n, 12m^2n^4, 20m^5 | 4 | m^2 | 4m^2 |
Formula Used
For monomials, the greatest common factor combines two ideas. First, find the greatest common divisor of all absolute coefficients. Second, compare the exponent of each variable across every monomial and keep the smallest exponent.
Formula:
GCF = gcd(|a1|, |a2|, ..., |an|) × ∏ vj^min(e1j, e2j, ..., enj)
Here, aj values are coefficients. Each vj is a variable. Each eij is the exponent of a variable in one monomial.
If a variable is missing from any monomial, its exponent is treated as zero, so it does not appear in the final GCF.
How to Use This Calculator
- Enter two or more monomials in the monomial box.
- Choose whether commas, lines, or semicolons separate the terms.
- Set a variable order if you want a custom display order.
- Choose whether uppercase and lowercase letters should match.
- Pick your output style.
- Click Calculate GCF.
- Review the result, exponent table, and graph.
- Download the result as CSV or PDF when needed.
Frequently Asked Questions
1. What is a monomial greatest common factor?
It is the largest monomial that divides every input monomial exactly. It includes the greatest common divisor of coefficients and the smallest shared exponents of common variables.
2. Why are missing variables treated as exponent zero?
A missing variable means that variable is not a factor in that monomial. Its exponent is zero, so the shared minimum becomes zero and the variable drops from the GCF.
3. Does the sign affect the coefficient GCD?
The calculator uses absolute coefficient values when finding the coefficient GCD. That matches standard algebra practice for greatest common factor calculations.
4. Can I enter terms on separate lines?
Yes. You can separate monomials with commas, line breaks, or semicolons, depending on the option you choose in the form.
5. What happens if I enter only constants?
The calculator still works. It finds the greatest common divisor of the constants, and the result contains no variable factor.
6. Can repeated variables appear in one monomial?
Yes. If you enter a variable more than once in one monomial, the calculator adds the exponents together when normalizing that term.
7. Why is the graph useful here?
The graph shows minimum exponents for variables, making it easier to see which variables survive into the final GCF and which ones drop out.
8. Can I export the results?
Yes. Use the CSV button for spreadsheet style output and the PDF button for a printable summary of the current calculation.