For a positive integer , the prime factorization of is an expression for as a product of powers of prime numbers. An important theorem of number theory called the Fundamental Theorem of Arithmetic tells us that every positive integer has a unique prime factorization, up to changing the order of the terms.
The prime factorization of 378 is .
, where n is any natural number, the are prime numbers, and the are their positive integral exponents. Prime factorizations are important in many ways, for instance, to simplify fractions.