Number Factorizations

Definition

Given a number $n \in \N $, a factorization $\pi = (\pi _1, \dots , \pi _p)$ of $n$ is a list of numbers in $\N $ satisfying

\[ n = \pi _1\cdot \pi _2\cdots\pi _p \]

We say that the factorization $\pi $ factors $n$ and we call $\pi _i$ a factor, and refer to the set $\set{\pi _1, \dots , \pi _p}$ as the factors.