Prime factorization calculator
Break a number into prime factors, list every factor, and check whether it is prime.
- ๐บ๐ธ US federal & state rules
Prime factorization of 360
2ยณ ร 3ยฒ ร 5
360 is composite
- Number of factors
- 24
- Sum of factors
- 1,170
- Previous prime
- 359
- Next prime
- 367
This is an example. Enter your numbers above and press the button to see your own result.
Result text
360 = 2^3 ร 3^2 ร 5
All 24 factors
| Factors | 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360 |
|---|
Show the math
| 360 รท 2 | 180 |
|---|---|
| 180 รท 2 | 90 |
| 90 รท 2 | 45 |
| 45 รท 3 | 15 |
| 15 รท 3 | 5 |
| 5 รท 5 | 1 (what was left is prime) |
| Number of factors | (3+1) ร (2+1) ร (1+1) = 24 |
What to do next
How it works
The calculator divides by 2, then 3, then numbers of the form 6k ยฑ 1, and stops as soon as what is left is prime. Every whole number above 1 has exactly one prime factorization, so the result does not depend on the order you divide in.
The factor list is built from the prime powers. The sum of factors uses the formula (p^(e+1) - 1) / (p - 1) for each prime power, multiplied together.
Things to keep in mind
Numbers up to 10^15 work. A number that is the product of two large primes takes the longest, and the calculator stops after a few seconds if it can't finish.
Frequently asked questions
What is the prime factorization of 360?
360 = 2ยณ ร 3ยฒ ร 5. Divide by 2 three times (360, 180, 90, 45), then by 3 twice (15, 5), and 5 is prime.
How many factors does a number have?
Add 1 to each exponent and multiply. 360 = 2ยณ ร 3ยฒ ร 5ยน has (3+1)(2+1)(1+1) = 24 factors.
Is 1 a prime number?
No. A prime has exactly two factors, 1 and itself. 1 has only one factor, so it is neither prime nor composite.
How do I know if a big number is prime?
Enter it here. The calculator runs a Miller-Rabin test that is exact for every number in its range, then shows the previous and next prime.