Prime Factorization Calculator
Break a whole number up to 10^18 into its prime factors, with exponents, the number of divisors and their sum.
Your inputs
Results
Prime factorization
2³ × 3² × 5
- Expanded
- 2 × 2 × 2 × 3 × 3 × 5
- Number of divisors
- 24
- Sum of divisors
- 1170
- Distinct prime factors
- 3
✓Exact calculation — rounded only for display
What this calculator does
Every integer above 1 is a unique product of primes. Factorization underpins simplification, GCD/LCM and number theory.
Formula and method
Trial division by small primes, then Pollard’s rho with Miller–Rabin for large factors. Divisors = Π(eᵢ + 1).
Worked example
Calculated by this tool with its default inputs:
Inputs
- Whole number (2 to 10^18): 360
Results
- Prime factorization: 2³ × 3² × 5
- Expanded: 2 × 2 × 2 × 3 × 3 × 5
- Number of divisors: 24
- Sum of divisors: 1170
- Distinct prime factors: 3
How to read the results
A prime number factorizes as itself.
Assumptions and limitations
- Large semiprimes with two big factors may take a moment.
Questions
How many divisors does 360 have?
360 = 2³ × 3² × 5, so (3+1)(2+1)(1+1) = 24.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 5 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy