Prime Factorization Calculator
One integer per line - factor it into primes with exponent form, divisor count and divisor sum
Output:
Separator:
Calculation Result
Download CSV
| No. | Original | Factorization | Exponent form | Divisors | Sum of divisors |
|---|
Introduction to the tool and how to use it
Prime factorization calculator splits integers into a product of primes, one number per line, with batch paste supported.
For example, 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2^3 × 3^2 × 5, with 24 divisors and a divisor sum of 1170.
The algorithm uses BigInt: small factors are first stripped using primes below 1000, then Miller-Rabin checks primality and Pollard rho splits composites; composites up to 18 digits are factored quickly. Composites that are too large to factor are skipped with a notice, so no wrong result is returned.
For example, 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2^3 × 3^2 × 5, with 24 divisors and a divisor sum of 1170.
The algorithm uses BigInt: small factors are first stripped using primes below 1000, then Miller-Rabin checks primality and Pollard rho splits composites; composites up to 18 digits are factored quickly. Composites that are too large to factor are skipped with a notice, so no wrong result is returned.
How to use
- Enter one integer per line, such as
360. - Choose the output format (product plus exponents / product only / exponents only).
- Click Start calculation; the result table shows both notations, divisor count, and divisor sum, with one-click copy and CSV export.
Factorization
Prime factorization of 123456789
123456789 = 3^2 × 3607 × 3803, which is 3 × 3 × 3607 × 3803 written out in full.
- Exponent form3^2 × 3607 × 3803
- Product form3 × 3 × 3607 × 3803
- Divisor count12
- Divisor sum178422816
Divisor list
| # | Divisor | Paired divisor |
|---|---|---|
| 1 | 1 | 123456789 |
| 2 | 3 | 41152263 |
| 3 | 9 | 13717421 |
| 4 | 3607 | 34227 |
| 5 | 3803 | 32463 |
| 6 | 10821 | 11409 |
| 7 | 11409 | 10821 |
| 8 | 32463 | 3803 |
| 9 | 34227 | 3607 |
| 10 | 13717421 | 9 |
| 11 | 41152263 | 3 |
| 12 | 123456789 | 1 |
- Divisors are listed in ascending order; the paired divisor is the one it multiplies with to give the original number.
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