将任意整数分解为质因数，显示完整的逐步解题过程、指数形式和因数个数。
Prime factorization is one of the most fundamental concepts in number theory — the mathematical study of integers and their properties. The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be expressed as a unique product of prime numbers. This uniqueness makes prime factorization indispensable across mathematics and computer science.
This calculator uses trial division — testing divisibility by each prime starting from 2 — to systematically find all prime factors. The result is displayed in exponential form and as a complete step-by-step division walkthrough.
In the digital age, prime factorization has taken on critical importance in cryptography. The RSA algorithm — which secures most internet communications — relies on the mathematical fact that while multiplying two large primes is trivial, factoring their product is computationally infeasible for large enough numbers.
Factorize 360: 360÷2=180 → 180÷2=90 → 90÷2=45 → 45÷3=15 → 15÷3=5 → 5 is prime. Result: 360 = 2³ × 3² × 5¹. Divisors: (3+1)(2+1)(1+1) = 24.