| Usually when we refer to a factor we mean a "non-trivial factor,"
which would then exclude this last example, and exclude considering
1 as a factor of anything. More generally, any element that is a factor
or everything else is called a "unit." |
A factor is something that divides into something else. Examples include:
- 7 is a factor of 91,
- (x-1) is a factor of $x^2-2x+1,$ and
- in a group G, the identity element, e, is a factor of everything.
If a number
N can be written as a (usually non-trivial) product,
so that N=pq,
then p and q are called factors of N.
By analogy, other mathematical objects: polynomials, matrices etc. can have factors.
The fundamental theorem of arithmetic says that the prime factors
of a number are, up to sign and reordering, unique.