Free 100% In-Browser Tool

Factoring Calculator

Find prime factors of integers and factor quadratic or polynomial expressions instantly.

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How to Use the Factoring Calculator

1Select whether you want to factor an integer number or an algebraic quadratic polynomial (ax² + bx + c).
2Enter your numbers or coefficients into the designated input fields.
3Review the factored expression, real or complex roots, and prime factorization tree.
4Click 'Copy Result' to paste the complete breakdown into your homework or study notes.

Formula & How It Works

Factoring Method & Prime Factorization

ax² + bx + c = a(x - r₁)(x - r₂)

For quadratic polynomials ax² + bx + c, the factoring method finds two numbers whose product equals a × c and sum equals b. For integers, trial division with prime numbers produces the unique prime factorization according to the Fundamental Theorem of Arithmetic.

Worked Examples

Quadratic Factoring Example

Input: x² + 5x + 6

Explanation: Numbers that multiply to 6 and add to 5 are 2 and 3, yielding (x + 2)(x + 3).

Result: (x + 2)(x + 3)

Integer Factoring Example

Input: 72

Explanation: 72 divides by 2 three times (leaving 9), which divides by 3 twice.

Result: 2³ × 3² (2 × 2 × 2 × 3 × 3)

Frequently Asked Questions

Can this factoring calculator factor non-factorable quadratics?▼

Yes. When a quadratic cannot be factored into integer coefficients, the calculator computes the exact discriminant (b² - 4ac) and identifies roots using the quadratic formula.

What is prime factorization?▼

Prime factorization is the decomposition of a composite integer into a product of prime numbers that uniquely identify the integer.

Does this tool work completely offline in my browser?▼

Yes, all calculation logic runs 100% in your browser using pure client-side TypeScript.

How do negative coefficients work?▼

You can enter negative coefficients directly into the inputs (e.g. b = -7, c = 12).

Last reviewed & updated: 2026-03-15

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