Prime Factorization Calculator
Break any integer into its prime factors using trial division. Shows factor list, exponent form, and primality check.
MATHBreak any positive integer into its prime factors via trial division. Shows the factor list, exponent form (e.g., 360 = 2³ × 3² × 5), and a primality check for the input itself.
By the Fundamental Theorem of Arithmetic, every integer greater than 1 is either prime or can be uniquely written as a product of primes. This factorization is the basis for the Euclidean algorithm, modular arithmetic, and RSA public-key cryptography. RSA security relies on the difficulty of factoring 2048-bit semiprimes.
Prime Factorization Calculator
Break any positive integer into its prime factors using trial division. Shows the factor list, exponent form, and whether the number is itself prime.
Fundamental Theorem of Arithmetic
Every integer greater than 1 is either prime, or can be uniquely written as a product of primes (up to ordering). This is the basis for the Euclidean algorithm, modular arithmetic, and RSA public-key cryptography. RSA security relies on the fact that factoring a 2,048-bit semiprime is computationally infeasible on classical hardware - while the calculator above easily handles 15-digit numbers in milliseconds.