Factoring Calculator
A factoring calculator is an online mathematical tool that breaks down numbers into their prime factors or decomposes algebraic expressions into simpler multiplied terms. By entering a whole number or a polynomial equation into the calculator, you instantly receive the complete list of factor pairs, prime factorization trees, or fully factored binomials without doing manual calculations.
Best for small numbers
Created by Ethan Park
Last updated: September 28, 2026
How to Use the Factoring Calculator
Using a factoring calculator takes only a few seconds and requires minimal effort. You simply type your number or algebraic expression into the input field and click calculate. The tool processes the input and generates the results immediately.
If you are working with large integers, you can also use a greatest common divisor calculator to find shared factors between multiple values. For advanced polynomial expressions, pairing this tool with an algebra solver helps verify complex root calculations.
Types of Factoring Calculations
Different math problems require different factoring methods. Knowing what kind of expression you have helps you choose the right approach.
Factoring Whole Numbers
Finding the factors of a whole number means identifying all integers that divide evenly into that number without leaving a remainder. For instance, the number 12 can be factored into pairs like 1 and 12, 2 and 6, or 3 and 4.
Prime Factorization
Prime factorization breaks a composite number down into a product of prime numbers that can only be divided by one and themselves. For example, the prime factorization of 60 is 2 squared times 3 times 5. You can check individual numbers using a prime number calculator to verify if they are prime.
Factoring Polynomials and Quadratics
Algebraic factoring rewrites a polynomial as the product of simpler terms. Quadratic expressions, which typically take the form of ax squared plus bx plus c, can often be factored into two binomials. If an equation cannot be easily factored by grouping, you can switch to a quadratic formula calculator to find the roots.
Step-by-Step Examples
Walking through manual examples helps clarify how the underlying math works before relying on automated tools.
Example 1: Finding Factors of 24
To find all positive factors of 24, test integers starting from 1 upward:
- 1 times 24 equals 24.
- 2 times 12 equals 24.
- 3 times 8 equals 24.
- 4 times 6 equals 24.
The complete list of factors is 1, 2, 3, 4, 6, 8, 12, and 24.
Example 2: Factoring a Quadratic Expression
To factor the quadratic expression x² + 5x + 6, find two numbers that multiply to 6 and add up to 5.
- The numbers 2 and 3 multiply to 6.
- The numbers 2 and 3 add up to 5.
- Rewrite the expression into binomial factors: (x + 2)(x + 3).
Frequently Asked Questions
What is a factor in math?
A factor is an integer that divides evenly into another number without leaving a remainder. For example, 3 is a factor of 12 because 12 divided by 3 equals 4 exactly.
What is the difference between factors and multiples?
Factors are numbers that divide evenly into a larger number, while multiples are numbers produced by multiplying a given number by integers. For example, factors of 4 are 1, 2, and 4, whereas multiples of 4 include 4, 8, 12, 16, and so on.
How do you factor a quadratic equation when a is greater than 1?
When the leading coefficient of a quadratic expression is greater than 1, you use the grouping method or the AC method. You multiply the leading coefficient by the constant term, find two numbers that add up to the middle coefficient, and split the middle term to factor by grouping.
Can negative numbers be factored?
Yes, negative numbers can be factored by including negative integer pairs or factoring out a negative one. For instance, negative 12 can be factored as negative 3 times positive 4.