Both Uses of

factor
in
The Lightning Thief

The reflection's size should be off by a factor of—†
Chpt 11

factor = thing that affects a result or outcome

There were just too many unknown factors.†
Chpt 17 *

factors = things that affect a result or outcome

Definitions:

(1) (factor as in: It was the deciding factor.)
something that affects a result or outcome

You also may encounter x-factor or x factor--meaning "the most important thing that influences a result or outcome."
(2) (factor as in: factor it into your thinking)
include consideration of
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

See a comprehensive dictionary for other meanings. Less common meanings include one that has to do with units of measurement. More specialized meanings are used in fields including mathematics, business, finance, biology, and grammar.