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Edit made on August 15, 2011 by ColinWright at 20:55:12
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[[[>40 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 EQN:x^2-2x+1, and
* in a group /G,/ the identity element, /e,/ is a factor of everything.
If a positive number N can be written as a product of positive numbers i.e. N = p x q (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.