Prime Factorization Calculator
Factor a positive integer up to one trillion. See prime powers, primality, divisor count, the exact divisor sum and a sorted divisor table.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Repeatedly divide by 2, then 3, then trial factors of the form 6k±1 up to the square root of the remaining value. The leftover value greater than 1 is prime. Generate the divisors from combinations of prime powers.
n = p₁^a₁ × … × pₖ^aₖ; divisor count = Π(aᵢ+1); divisor sum = Π(1+pᵢ+…+pᵢ^aᵢ)
Worked example
360 = 2³ × 3² × 5. It has (3+1)(2+1)(1+1) = 24 positive divisors. Their sum is (1+2+4+8)(1+3+9)(1+5) = 1170.
Assumptions and input details
Enter ordinary decimal integer digits, without commas, fractions, exponent notation or a minus sign. The value 1 has no prime factors, one positive divisor and is neither prime nor composite. Trial division is deterministic within the stated one-trillion limit; this is not a cryptographic-size factoring service. The divisor table shows the first 100 sorted positive divisors when there are more; the count and sum include all divisors.
References: OpenStax: prime and composite numbers
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Fraction, counting, number-base and integer-factor results use exact integer arithmetic. Any decimal or percentage display is approximate.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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