I know of the following terms:
- A proper factor of a positive integer $n$ is a factor of $n$ other than $1$ or $n$.
- A proper divisor of a positive integer $n$ is a factor of $n$ other than $n$ (but including $1$).
But is there a known or used term for the following?
- _____ of a positive integer $n$ is a factor of $n$ other than $1$ (but including $n$).
Or anything similar that can substitute "factors of $n$ other than $1$" ?
For example, say the term "_____" was "whole factor".
Then, I would be able to write "partitions of numbers into whole factors".
For example, all such partitions of $30$ are $30 = 15\cdot2 = 10\cdot3 = 6\cdot5 = 2\cdot3\cdot5$.
But instead of inventing my own word for it such as the above example, I would prefer if there was already an established definition already being used in some context or topics.
Edit: After some discussion in the comments, it appears that "Unordered Factorization" does not include the factor $1$ by its definition and fits the context in my earlier examples. (In case this is useful for someone that could have a similar question as me in the future.)
How about nontrivial factor?
On this Massey University site, for example, they define a trivial factor of $n$ to be $1$, and an improper factor to be $n$ itself.
Some sources use trivial to refer to both $1$ and $n$, so whatever term you use, it would be best to make your definition explicit.