Online Tool Store
Prime Factorization Tool
Factorize any integer into its prime factors instantly, shown both as a full multiplication and in exponent notation. Runs entirely in your browser.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Prime factorization
Unique prime factors
How it works
- Enter any integer of 2 or greater.
- The tool divides it by increasing prime candidates until only prime factors remain.
- Results are shown both as a full multiplication and grouped into exponent notation.
The formula
Trial division: starting at 2, repeatedly divide the number by the smallest possible divisor until what remains is 1, checking divisors only up to the square root of the remaining value for efficiency.
FAQ
What is prime factorization?
Breaking a number down into the set of prime numbers that multiply together to produce it — every integer greater than 1 has exactly one such factorization.
Why does the exponent notation matter?
Writing 360 as 2³ × 3² × 5 instead of 2 × 2 × 2 × 3 × 3 × 5 makes it immediately clear how many times each prime factor repeats, which is useful for finding GCD/LCM.
Is there a limit to how large a number I can factorize?
This uses trial division, which stays fast up to about a trillion — much larger numbers (especially ones with large prime factors) would need a more advanced algorithm.
Is my number sent anywhere?
No — factorization runs entirely with JavaScript in your browser.
How we compare
| Feature | Online Tool Store | WolframAlpha | Manual division |
|---|---|---|---|
| No sign-up | ✓ | ✓ | ✓ |
| Instant as-you-type result | ✓ | ✗ | ✗ |
| Exponent notation shown | ✓ | ✓ | ✗ |
If you're checking homework or just curious about a number's structure, this gives you the answer instantly without a general-purpose math engine.