How to Use
- 1.
Choose Number factors to enter one integer and review its prime factors, factor pairs, and prime or composite status.
- 2.
Enter two to twelve integers in the GCF and LCM field, separated by commas or spaces.
- 3.
Choose Polynomials and enter an expression using x^2 notation or the exponent helper buttons.
- 4.
Review the factored form, expanded verification, and explanation; use an example button to load a common pattern.
- 5.
Choose Practice, select a difficulty, enter your own answer, and check it against the generated problem.
- 6.
Copy a result or download the displayed solution as a text file for study notes.
Features
Prime factorization, positive factor pairs, and prime/composite check
Exact GCF and LCM for two to twelve whole numbers
Polynomial factoring for common factors, quadratics, squares, and many cubics
Expanded-form verification to confirm the factors match the input
Pattern explanation and step-by-step solution notes
Visual prime factor tree for composite integers
Basic, intermediate, and advanced practice problems with instant feedback
Built-in reference for common factoring identities
Copy results and download study steps as a text file
Client-side calculations; expressions are not uploaded
Frequently Asked Questions
How do I factor a polynomial online?+
Choose Polynomials, enter an expression such as x^2 + 5x + 6, and review the factored form. The calculator expands the result again to verify that it matches your expression.
Can this factoring calculator show steps?+
Yes. It shows the input, the factorization, an expanded verification, and a short explanation of a recognized pattern. The explanation is a study aid; write out any additional reasoning your course requires.
How do I find the prime factors of a number?+
Choose Number factors and enter a whole number. The result lists prime factors with multiplicity, positive factor pairs, and whether the number is prime or composite.
Can I calculate GCF and LCM for more than two numbers?+
Yes. Enter between two and twelve whole numbers, separated by commas or spaces, to calculate both the greatest common factor and least common multiple.
Does it factor every polynomial?+
No symbolic factoring tool can express every polynomial in simple rational factors. This calculator handles many common integer and rational polynomial forms; an irreducible expression may remain unchanged or be reported as unsupported.
Can I enter negative numbers?+
Yes. Integer factorization shows the sign separately from the prime factors of the magnitude, and GCF/LCM calculations accept negative integers. Polynomial expressions can also include subtraction and negative coefficients.
Are my expressions uploaded or saved?+
No. Factoring runs in your browser, and the calculator does not upload or save the expressions you enter.
What is the difference between prime factorization and polynomial factoring?+
Prime factorization writes an integer as a product of prime numbers. Polynomial factoring rewrites an algebraic expression as a product of simpler expressions, such as x^2 + 5x + 6 = (x + 2)(x + 3).
About this tool
Free Factoring Calculator
Use this factoring calculator to find the prime factorization and factor pairs of an integer, calculate the greatest common factor (GCF) and least common multiple (LCM), or factor a polynomial. Results are checked by expanding the factors, and practice mode gives you new problems with answer feedback.
## Factor a Polynomial and Verify the Result
Enter an expression such as x^2 + 5x + 6, 2x^2 + 4x, or x^2 - 9. The calculator recognizes common factors, quadratic expressions, difference-of-squares patterns, and many cubic or higher-degree expressions over rational coefficients. It returns the factored form, an expanded check, and an explanation of the pattern when one can be identified. Some polynomials are irreducible over the supported rational forms, so a result may remain unchanged.
## Prime Factorization and Factor Pairs
Enter a whole number to see its prime factors, positive factor pairs, and whether it is prime or composite. Negative values are handled by factoring the magnitude and showing the negative sign separately. Zero has no finite prime factorization. Integer calculations support inputs from −1 trillion through 1 trillion.
## Find the GCF and LCM of Several Numbers
Enter two to twelve whole numbers to calculate their greatest common factor and least common multiple. The results use exact integer arithmetic, including for negative inputs. When any input is zero, the GCF follows the standard common-divisor definition and the LCM is zero.
## Practice Factoring Step by Step
Choose a basic prime-factor problem, an intermediate quadratic, or an advanced cubic. Submit your own factorization to check whether expanding it reproduces the original expression. The built-in formula reference covers common factors, difference of squares, perfect-square trinomials, and sums or differences of cubes.
Calculations run in your browser; entered expressions are not sent to a factoring service. This educational tool is not a substitute for showing the reasoning required by a class or assignment. Browse the full set of math and finance options in our [Calculators category](/category/calculators).
For functions defined by interval-specific rules, continue with the Piecewise Function Calculator. Explore more practical tools in the Calculators category.