Prime Number Checker
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Prime numbers are the building blocks of all natural numbers — every integer greater than 1 can be uniquely expressed as a product of primes, a result known as the Fundamental Theorem of Arithmetic.
This tool checks whether a given number is prime and, if it is not, shows its complete prime factorization. Understanding prime numbers is essential in number theory, cryptography, and computer science. They play a key role in encryption algorithms like RSA that secure modern internet communications.
How it works
A number n is prime if it has exactly two distinct divisors: 1 and n. Trial division checks divisibility by all integers from 2 up to √n. Prime factorization expresses n as a product of prime powers: n = p₁^a₁ × p₂^a₂ × ... × pₖ^aₖ.
Use cases
- Checking if a number is prime for math homework or competitions
- Finding the prime factorization of composite numbers
- Understanding number theory concepts like GCD and LCM
- Learning about the building blocks of cryptographic algorithms