TITLE: Definition of factor - Is n a factor of n?
QUESTION [5 upvotes]: Is there a universally agreed upon definition of what a factor of a number is?
Is $n$ a factor of $n$?
Is $1$ a factor of $n$?
EDIT x 2: Integers Natural Numbers

REPLY [3 votes]: Yes, $1$ and $n$ are, trivially, factors or divisors of $n$.  In particular, if $n$ is a prime number, then the prime factorization of $n$ is simply $n$ itself.
That said, when speaking of the factors of a number, it is often useful to exclude these trivial factors.  The usual term for that is "proper factor" or "proper divisor".  Specifically, a proper divisor of a number $n$ is normally defined to be any divisor of $n$ which is strictly greater than $1$ and less than $n$.  In particular, this means that prime numbers do not have proper divisors, whereas all composite numbers do.