About GCF of a Polynomial Calculator
This calculator finds the greatest common factor of the terms of a polynomial and writes the expression as that factor times what is left. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The common factor is the greatest common divisor of the coefficients times the lowest power of x present in every term. The page opens on 6x² + 9x: the numbers share 3, and both terms contain x, so the GCF is 3x and the result is 3x(2x + 3).
Taking out the GCF first is the first step of almost every factoring problem, and it often makes the rest easy. The calculator then keeps factoring what is left.
How to use GCF of a Polynomial Calculator
- Pick Polynomial or Whole number.
- For a polynomial, type it using ^ for powers, for example x^3 + x^2 + 2x + 2, or use the keypad.
- Read the factored form at the top. It updates as you type.
- Open the steps to see each method applied, and the expansion check underneath.
- For a whole number, read the factor pairs, the full list of factors and the prime factorization.
Features
- Greatest common factor taken out first, including numbers and powers of x.
- Difference of squares, sum of cubes and difference of cubes recognised by pattern.
- Perfect square trinomials and general trinomials through the rational root theorem.
- Factoring by grouping for four-term polynomials.
- Repeated application, so x⁴ - 16 splits into (x - 2)(x + 2)(x² + 4).
- An expansion check that multiplies the factors back out.
- Whole-number mode with factor pairs, all factors and the prime factorization.
- Math keypad and live preview, usable on a phone.
Greatest common factor
Take the GCD of the coefficients and the smallest exponent of each shared variable.
GCF(6x², 9x) = 3x
6x² + 9x = 3x(2x + 3)Worked examples
6x² + 9x gives 3x(2x + 3)
GCF of 6 and 9 is 3, and both terms have x.
3x³ - 12x gives 3x(x - 2)(x + 2)
Take out 3x, then factor x² - 4 as a difference of squares.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The expressions you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Always take out the greatest common factor first. It often turns a hard trinomial into an easy one.
- Multiply your factors back out to check them. The calculator does this for you under the steps.
- If a quadratic is irreducible over the rationals, its discriminant is not a perfect square. Try the quadratic formula calculator for its exact roots.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Expressions are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Expressions are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I find the GCF of a polynomial?
Find the greatest common divisor of the coefficients, then multiply by the lowest power of the variable that appears in every term.
Can the GCF be just a number?
Yes. In 4x² + 6x + 10 the GCF is 2, because the terms share no power of x.
More Factoring Calculator pages
- Factoring CalculatorType a polynomial to factor it with every step, or switch to a whole number for its factor pairs.
- Factor Trinomials CalculatorType a trinomial and get its two factors with the working.
- Difference of Squares CalculatorType an expression like 4x² - 25 and see it factored as a difference of squares.
- Sum and Difference of Cubes CalculatorType a cubic like 27x³ + 8 and see it factored with the cube formulas.
- Factor by Grouping CalculatorType a four-term polynomial and see it factored by grouping.
- Perfect Square Trinomial CalculatorType a trinomial and see whether it is a perfect square.
- Factor Pairs CalculatorEnter a whole number to get all its factor pairs and factors.