Prime factorization
Break an integer from 2 to 10¹² into its prime factors; 360 = 2³ × 3² × 5.
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- Instant result
Assumptions & formula
Formula and assumptions
n = ∏ pᵢ^eᵢ; 2≤n≤10¹²
Results
Enter values and press Calculate to see the result here.
How to use this calculator
- Set inputs and units
Enter an integer from 2 to 10¹². Factorization repeatedly divides by prime factors.
- Calculate
Check this worked example: 360 → 2^3 ×3^2 ×5; 8×9×5=360
- Results
Multiply the prime powers to rebuild the input. If only one factor comes back, the number itself may be prime.
Questions and limits
Why can large primes take longer?
Trial division tests 2 and the odd divisors up to the square root of what remains. The upper bound keeps that work finite.
Which input errors should I correct?
Don't enter decimals, negative numbers, zero or 1. They are outside the domain of prime factorization used here.
What does this calculation leave out?
Limited exact integer factorization. It is not cryptographic key analysis or primality testing for numbers of any size.