Prime factorization
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.