Need to factor a number for math class? Or break down a polynomial into simpler terms?

This Factorization Calculator handles both — prime factorization for integers and polynomial factorization for quadratic expressions. Just type in your number or expression, hit a button, and get your answer instantly.

No downloads. No sign-ups. Just fast, accurate results.

Factorization Calculator — Try It Now

How to Use This Tool

This calculator has two functions. You can use one or both at the same time.

For Prime Factorization (Numbers):

1. Enter any positive integer in the first field (e.g., 140)
2. Click “Execute”
3. Your prime factors appear instantly with exponents

For Polynomial Factorization:

1. Enter a quadratic expression in the second field
2. Use the format: x^2+4x+4 (use ^ for exponents)
3. Click “Execute”
4. The factored form appears below

Other Controls:

• Press Enter on your keyboard to run the calculation
• Click “Clear” to reset everything and start fresh

Works the same on desktop and mobile — no app needed.

Example Calculations

Prime Factorization Example:

• Input: 140
• Result: 2² × 5 × 7

This tells you that 140 = 2 × 2 × 5 × 7.

Polynomial Factorization Example:

• Input: x^2+4x+4
• Result: (x+2)(x+2)

This means x² + 4x + 4 factors into (x + 2) squared.

Understanding Your Results

Prime factorization results show each prime factor with its exponent. If you see 2³, that means 2 appears three times (2 × 2 × 2). Multiply all the factors together to get back to your original number.

Polynomial results show the expression broken into binomial factors. You can verify by multiplying the factors back together using FOIL.

How Factorization Works

Prime Factorization Explained

Every integer greater than 1 can be written as a product of prime numbers. This is called the Fundamental Theorem of Arithmetic.

The calculator uses trial division: it starts with the smallest prime (2) and divides repeatedly until that prime no longer works, then moves to the next prime (3, 5, 7, etc.) until the number is fully broken down.

For example, 60 breaks down like this: 60 ÷ 2 = 30, 30 ÷ 2 = 15, 15 ÷ 3 = 5, and 5 is prime. So 60 = 2² × 3 × 5.

Polynomial Factorization Basics

Polynomial factorization reverses the multiplication of binomials. For a quadratic like x² + bx + c, the calculator finds two numbers that add up to b and multiply to c.

This tool handles standard quadratics with integer solutions. For more complex polynomials (cubic, non-integer roots), you may need specialized software.

Frequently Asked Questions（FAQ）

What numbers can I factor?

Any positive integer works. The calculator handles very large numbers, though extremely large values may take a moment to process.

Why won’t my polynomial factor?

Not all polynomials factor neatly into integers. If the discriminant (b² – 4c) isn’t a perfect square, the polynomial doesn’t have integer roots. The tool will display “Unable to factor” in these cases.

Is this accurate for homework?

Yes — the prime factorization is mathematically exact. For polynomials, always verify by multiplying your factors back together.

Can I use this on my phone?

Absolutely. The tool is fully responsive and works in any mobile browser.

What’s the difference between factoring and prime factoring?

“Factoring” can mean breaking something into any factors (like 12 = 3 × 4). “Prime factoring” specifically means breaking it into prime numbers only (12 = 2² × 3).

Important Notes

This calculator provides accurate results for standard cases, but keep in mind:

• Polynomial factorization is limited to quadratics with integer coefficients and integer solutions
• For academic work, always show your steps — don’t just copy the answer
• This tool is for reference and learning; verify important calculations independently

Bookmark This Tool

Factorization problems pop up constantly in algebra, number theory, and standardized tests. Save this page for quick access whenever you need to break down a number or simplify a polynomial.

More math tools coming soon — check back for calculators covering GCD/LCM, quadratic formula, and more.