Prime Factorization Calculator — Formula

## Prime Factorization

### What Is It?

Every integer greater than 1 can be written as a product of prime numbers in exactly one way (Fundamental Theorem of Arithmetic).

### Method: Trial Division

1. Start with the smallest prime (2)
2. If it divides the number, it is a factor; divide and repeat
3. If not, try the next prime (3, 5, 7, 11, ...)
4. Stop when you reach sqrt(n)

### Divisibility Quick Checks

- **By 2**: last digit is even
- **By 3**: digit sum is divisible by 3
- **By 5**: last digit is 0 or 5

This calculator shows divisibility checks. For full factorization of large numbers, a step-by-step approach is needed.