Prime Factorization Calculator
Last updated: November 5, 2026
Break a positive whole number into prime factors and review divisor information.
Prime factorization
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- Is the number prime?: —
- Number of positive divisors: —
- Sum of distinct prime factors: —
On this page
Quick summary: Break a positive whole number into prime factors and review divisor information.
Read the complete guide
Updated reference sections in this guide are in English.
What this calculator estimates
Break a positive whole number into prime factors and review divisor information.
How to use it
Enter Whole number (2–1,000,000,000). Select Calculate to update the results.
How the calculation works
Trial division removes each prime factor repeatedly until the remaining value is prime.
Worked example: starting scenario
| Whole number (2–1,000,000,000) | 360 |
|---|
| Prime factorization | 2^3 × 3^2 × 5 |
|---|---|
| Is the number prime? | No |
| Number of positive divisors | 24 |
| Sum of distinct prime factors | 10 |
Important limitations
The input is capped at one billion so trial division remains fast in a browser.
Exponents count repeated prime factors
For 360, the factorization is 2³ × 3² × 5. The distinct-prime sum is 2 + 3 + 5 = 10, not the sum with repeated factors. The positive-divisor count is (3+1)(2+1)(1+1) = 24. A prime number has only itself in the factorization and exactly two positive divisors. This browser routine accepts integers from 2 through 1,000,000,000.