## Most recent change of Factor

Edit made on August 15, 2011 by ColinWright at 20:55:12

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HEADERS_END

[[[>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.