Prime Factorization Calculator
One integer per line - factor it into primes with exponent form, divisor count and divisor sum
Output:
Separator:
Calculation Result
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| 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 5040
5040 = 2^4 × 3^2 × 5 × 7, which is 2 × 2 × 2 × 2 × 3 × 3 × 5 × 7 written out in full.
- Exponent form2^4 × 3^2 × 5 × 7
- Product form2 × 2 × 2 × 2 × 3 × 3 × 5 × 7
- Divisor count60
- Divisor sum19344
Divisor list
| # | Divisor | Paired divisor |
|---|---|---|
| 1 | 1 | 5040 |
| 2 | 2 | 2520 |
| 3 | 3 | 1680 |
| 4 | 4 | 1260 |
| 5 | 5 | 1008 |
| 6 | 6 | 840 |
| 7 | 7 | 720 |
| 8 | 8 | 630 |
| 9 | 9 | 560 |
| 10 | 10 | 504 |
| 11 | 12 | 420 |
| 12 | 14 | 360 |
| 13 | 15 | 336 |
| 14 | 16 | 315 |
| 15 | 18 | 280 |
| 16 | 20 | 252 |
| 17 | 21 | 240 |
| 18 | 24 | 210 |
| 19 | 28 | 180 |
| 20 | 30 | 168 |
| 21 | 35 | 144 |
| 22 | 36 | 140 |
| 23 | 40 | 126 |
| 24 | 42 | 120 |
| 25 | 45 | 112 |
| 26 | 48 | 105 |
| 27 | 56 | 90 |
| 28 | 60 | 84 |
| 29 | 63 | 80 |
| 30 | 70 | 72 |
| 31 | 72 | 70 |
| 32 | 80 | 63 |
| 33 | 84 | 60 |
| 34 | 90 | 56 |
| 35 | 105 | 48 |
| 36 | 112 | 45 |
| 37 | 120 | 42 |
| 38 | 126 | 40 |
| 39 | 140 | 36 |
| 40 | 144 | 35 |
| 41 | 168 | 30 |
| 42 | 180 | 28 |
| 43 | 210 | 24 |
| 44 | 240 | 21 |
| 45 | 252 | 20 |
| 46 | 280 | 18 |
| 47 | 315 | 16 |
| 48 | 336 | 15 |
| 49 | 360 | 14 |
| 50 | 420 | 12 |
| 51 | 504 | 10 |
| 52 | 560 | 9 |
| 53 | 630 | 8 |
| 54 | 720 | 7 |
| 55 | 840 | 6 |
| 56 | 1008 | 5 |
| 57 | 1260 | 4 |
| 58 | 1680 | 3 |
| 59 | 2520 | 2 |
| 60 | 5040 | 1 |
- Divisors are listed in ascending order; the paired divisor is the one it multiplies with to give the original number.
Common inputs
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