Prime factorization : A prime factorization of a natural number writes the natural number as a product of prime factors. A prime factorization is usually stated in the form $n=\prod p_i^{n_i}.$ For example the prime factorization of 12 is $12=2^2\cdot 3.$ The fundamental theorem of arithmetic says that every number has a unique prime factorization (disregarding the order of the factors).