Prime Factorization
Find the prime factors of any number. Also shows all divisors, divisor count, and divisor sum.
Enter a positive integer
Puzzle Tips
- • Prime factors might be coordinate digits
- • Divisor count/sum often appear in formulas
- • Perfect squares, cubes have special factorizations
- • Factorization helps with modular arithmetic
What is Prime Factorization?
Prime factorization is the process of finding which prime numbers multiply together to make a given number. Every integer greater than 1 can be uniquely expressed as a product of primes (Fundamental Theorem of Arithmetic).
How It Works
Algorithm
- Start with the smallest prime (2)
- Divide the number by 2 as many times as possible
- Move to the next prime and repeat
- Continue until the remaining number is 1
Example: 360
360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
Related Calculations
Divisor Count (τ)
If n = p₁^a₁ × p₂^a₂ × ..., then the number of divisors is (a₁+1) × (a₂+1) × ...
Divisor Sum (σ)
The sum of all divisors. A number is "perfect" if σ(n) - n = n (e.g., 6 = 1 + 2 + 3, 28 = 1 + 2 + 4 + 7 + 14).
In Geocaching Puzzles
Prime factorization appears in puzzles:
- Factor extraction: Use specific factors as digits
- Divisor puzzles: Count or sum divisors
- Perfect numbers: 6, 28, 496 are special
- Cryptography themes: RSA and similar puzzles