The Unique Building Blocks of a Number

Every whole number greater than one can be written as a product of primes in exactly one way — the fundamental theorem of arithmetic. This prime factorization calculator applies trial division to find that unique form, from simple cases like 360 = 2³ × 3² × 5 to numbers up to nine quadrillion.

More Than a String of Factors

The exponent pattern immediately yields the number of divisors, their sum, and the largest prime factor. These flow straight from the factorization: each exponent e contributes a factor of (e + 1) to the divisor count and (p^(e+1) − 1)/(p − 1) to the divisor sum.

Why Prime Factors Matter

Factorization sits beneath GCD and LCM work, radical simplification, and perfect-number checks. It is also the mathematical heart of RSA encryption — large numbers are easy to multiply together but hard to factor back apart.