Prime Factorization Calculator – Find Prime Factors
Break a number into its prime factors, with an exponent form.
About the Prime Factorization Calculator
What is the Prime Factorization Calculator?
A prime factorization calculator expresses a whole number as a product of its prime factors.
Why use this calculator?
Every integer greater than 1 has one unique prime factorization. It powers GCD, LCM, simplification and modular arithmetic.
How to use it
- Enter a whole number of 2 or more.
- Read the expanded product of primes.
- See the compact exponent form too.
Formula
Trial division by primes up to √n.
By the Fundamental Theorem of Arithmetic the factorization is unique for integer inputs.
Frequently Asked Questions
What is a prime number?
A whole number greater than 1 that divides only by 1 and itself.
Why does the order of factors matter?
Multiplication is commutative, so order never matters; the exponent form just groups repeated primes.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.
How accurate are the results?
We use standard, widely accepted formulas and calculate in your browser using double-precision arithmetic. Results are rounded for readability, so treat them as reliable estimates rather than a guarantee. Real-world factors can vary the true figure.
Can I add this calculator to my own website?
Yes. Open this calculator page and use the "Add to your website" box in the sidebar to copy a ready-made iframe snippet, then paste it into any HTML page.
Does it work on a phone or tablet?
Yes. The layout is fully responsive, so it works on desktops, laptops, tablets and mobile phones, and every input adapts to touch screens.