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 form of a prime factorization 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. One instance is to simplify fractions.
Contents
[hide]Example Problem
The prime factorization of 378 is .
Resources
Books
Games