Every integer > 1 has a unique prime factorization (Fundamental Theorem of Arithmetic). 360 = 2³ × 3² × 5. The number of divisors is (3+1)(2+1)(1+1) = 24. Sum of divisors: σ(n) = Π(pᵉ⁺¹−1)/(p−1).
How to Use
Enter a positive integer:
- Input: Any integer ≥ 2
- Output: Prime factorization
- Extra: Divisor count and sum
Algorithm
Trial division: divide by 2, then odd numbers 3, 5, 7, ... up to √n. Each time a factor is found, divide repeatedly until it no longer divides. Any remainder > 1 is a prime factor.
Fundamental Theorem
Every integer > 1 is either prime or a unique product of primes (up to ordering). This is why primes are the 'atoms' of number theory.
Step-by-Step Instructions
- 1Enter a positive integer.
- 2View prime factorization.
- 3Check exponent form.
- 4See divisor count.
- 5Review divisor sum.