What is prime factorization?

Every integer greater than 1 can be written uniquely as a product of primes (fundamental theorem of arithmetic). E.g. 360 = 2³ × 3² × 5.

What algorithm is used?

Trial division by 2, then by odd numbers up to √n, with a 6k ± 1 wheel for efficiency. This is fast for numbers up to ~10¹⁵.

What is the difference between Ω(n) and ω(n)?

ω(n) is the number of distinct prime factors; Ω(n) is the total count with multiplicity. E.g. for 360 = 2³·3²·5, ω = 3 and Ω = 6.

Can I factor very large numbers?

For numbers above 10¹⁵ trial division can be slow. Real-world factorization of 200-digit numbers requires sophisticated algorithms (quadratic sieve, GNFS).

Is the calculation done locally?

Yes — entirely in your browser.

Prime Factorization Calculator

Break any integer into its prime factors — 2² × 3 × 5, etc.

100% private — no uploads Free & unlimited Read tutorial

See how it works

Watch a quick simulation of this tool in action — no file needed.

How to use Prime Factorization Calculator

Follow these steps — everything happens instantly in your browser.

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Step 1. Enter a positive integer (up to ~10¹⁵).
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Step 2. See the prime factorization (e.g. 360 = 2³ × 3² × 5) update instantly.
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Step 3. Distinct primes and the total number of prime factors are shown below.

Why use this tool

Frequently asked questions

Everything you might want to know about prime factorization calculator.

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