# factor

### General

The factors of a natural number $$n$$ are those whole numbers which divide it evenly. Since every number is divisible by itself and 1, neither 1 nor $$n$$ is considered a proper factor of $$n$$.

More generally, if an expression can be written as a product of other expressions, then those other expressions are its factors. For instance, a polynomial with rational coefficients may always be factored into a product of first and/or second degree polynomial factors.

A number (or other expression) with no proper factors is called prime.

### Graph Theory

A factor of a graph is a spanning subgraph having at least one edge. In many contexts, it is interesting to determine whether some graph $$G$$ can be decomposed into the edge-disjoint union of factors with some prescribed property. Such a decomposition is called a factorization of $$G$$. Often, the property in question is regularity of degree $$k$$. In this case, the factors are called $$k$$-factors, and the factorization a $$k$$-factorization. If $$G$$ has a $$k$$-factorization, it is called $$k$$-factorable.