Complete guide
Prime factorization calculator with powers, divisors and factor pairs
Enter an integer from 2 to one trillion. Calculator24 returns its unique prime-power decomposition, factor multiplicities, divisor count, factor sum and positive factor pairs.
What prime factorization means
A composite positive integer can be written as a product of primes. Apart from order, that factorization is unique.
Repeated division method
Start with 2 and divide while the remainder is zero, then try increasing candidate divisors. Once the candidate exceeds the square root of the remaining value, that remainder is prime.
Exponential notation
Repeated factors are grouped as powers. Three factors of 2 become 2³.
360=2³×3²×5Number of positive divisors
For prime exponents a, b and c, a divisor can choose each exponent from zero through its maximum.
d(n)=(a+1)(b+1)(c+1)…Worked factor-pair example
The factor pairs of 36 are 1×36, 2×18, 3×12, 4×9 and 6×6; all arise from its prime form 2²×3².
Computational scope
Trial division is practical for the stated one-trillion cap. Factoring cryptographic-size semiprimes is a different computational problem.
Prime-factor example
| Integer | Expanded factors | Prime powers |
|---|---|---|
| 36 | 2×2×3×3 | 2²×3² |
| 84 | 2×2×3×7 | 2²×3×7 |
| 360 | 2×2×2×3×3×5 | 2³×3²×5 |
Frequently asked questions
Is 1 a prime number?
No. One is neither prime nor composite.
What if the input is prime?
The factorization is the number itself.
Is prime factorization unique?
Yes for positive integers greater than one, apart from factor order.
How many divisors does 360 have?
It has 24 positive divisors.
Can I factor a decimal?
No. Enter a whole integer.
Can this factor cryptographic keys?
No. Its educational input limit is one trillion.
What to keep in mind
Positive integers from 2 through one trillion are supported. Trial division is deterministic here; this is an educational arithmetic tool, not a cryptographic factorization service.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.