Factoring Calculator

Factoring Calculator

Enter any polynomials or a non-zero integer, and the tool will instantly reduce it to simple factor pairs.

Our Factoring Calculator helps you factor any integer (positive or negative) and algebraic expressions like polynomials, binomials, and trinomials. It simplifies complex expressions and numbers into a product of simpler factors. You can also generate a factor tree and see step-by-step calculations.

What Is Factoring?

Factoring is the process of expressing a number or a polynomial as a product of its factors.

How To Factor Polynomials?

Factoring polynomials can be done in a few simple steps:

Identify the Greatest Common Factor (GCF) in the polynomial.
If a GCF exists, factor it out from the polynomial.

How To Factor Trinomials?

Trinomial factorization converts a second-degree equation of the form \(ax^2 + bx + c\) into a product of two binomials. For example:

x^2 + 8x + 12
= x(x + 2) + 6(x + 2)
= (x + 2)(x + 6)

The calculator simplifies this process: just enter the expression, and it finds the factors instantly.

What Is a Factor of a Number?

Factors of a number are numbers that divide it exactly. For example, 15 has factors 3 and 5 because 3 × 5 = 15. Some numbers have multiple factorizations. For example, 24 has factors 1, 2, 3, 4, 6, 8, 12, and 24, which can form pairs like 1×24, 2×12, 3×8, or 4×6.

How to Find Factors (Step-by-Step)

Example:

Find the factors of 18 and 12.

Solution:

Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 12: 1, 2, 3, 4, 6, 12
Prime factors of 18: 2 × 3 × 3
Prime factors of 12: 2 × 2 × 3
Factor pairs of 18: (1,18), (2,9), (3,6)
Factor pairs of 12: (1,12), (2,6), (3,4)
Common factors of 18 and 12: 1, 2, 3, 6

Properties of Factors

1 is a factor of every number.
Every number is a factor of itself.
Every factor is less than or equal to the number.
The total number of factors is always finite.

How the Factoring Calculator Works

The calculator is free and instantly finds the factors of any number or polynomial expression. Here's how to use it:

Choose "Integer Factoring" or "Polynomial Factoring".
Enter the number or expression.
Click Calculate.

Output: The calculator will provide:

Factors of the expression
Factors of a number
Prime factors of a number
Factor pairs of numbers
Common factors
Prime factor tree

FAQ

What Is a Common Factor?

A common factor is a number that is a factor of two or more numbers.

Factors of Common Numbers

Number	Factors
1	1
2	1, 2
3	1, 3
4	1, 2, 4
5	1, 5
6	1, 2, 3, 6

References

From Wikipedia: Expressions, History of factorization, Common factor, Grouping.
From Mesacc: Factoring Strategies, Adding and subtracting terms, Binomial expansions.