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 can factor integers (positive or negative) and algebraic expressions, including polynomials, binomials, and trinomials. It breaks down complex expressions into simpler factors and can generate a factor tree with step-by-step explanations.

What Is Factoring?

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

How to Factor Polynomials?

Factoring polynomials generally involves the following steps:

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

How to Factor Trinomials?

Trinomials of the form ax² + bx + c can often be factored into the product of two binomials. For example:

x² + 8x + 12
= x(x + 2) + 6(x + 2)
= (x + 2)(x + 6)

With our calculator, you can input the trinomial, and it will return the factors instantly.

What Is a Factor of a Number?

Factors of a number are integers that divide the number exactly without leaving a remainder. For instance, 15 has factors 3 and 5 because 3 × 5 = 15. Numbers often have multiple factors. For example, 24 has factors 1, 2, 3, 4, 6, 8, 12, 24, which can form pairs like 1×24, 2×12, 3×8, and 4×6.

Finding 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 integer.
Every number is a factor of itself.
All factors are less than or equal to the number.
The number of factors for any integer is always finite.

How the Factoring Calculator Works

This free calculator can instantly find factors for numbers and polynomial expressions. Steps:

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

Output Includes:

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

FAQ

What Is a Common Factor?

A common factor is a number that evenly divides 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
7	1, 7
8	1, 2, 4, 8
9	1, 3, 9
10	1, 2, 5, 10

References

From Wikipedia: Factorization, History, Common factor, Grouping.
From Mesacc: Factoring Strategies, Binomial and Polynomial Factorization.