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What is a factorization?

What is a factorization? Here are some definitions.

Noun
  1. (mathematics) The process of creating a list of factors.
  2. (mathematics) An expression listing items that, when multiplied together, will produce a desired quantity.
  3. A list of factors. (Can we add an example for this sense?)
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Examples
I mean, sure it's hard to do this prime factorization stuff, whatever you say it is.
The following section discusses two indicators of energy efficiency: energy intensity and an energy efficiency measure using factorization.
To isolate the effect of energy efficiency in the economy, as well as in individual sectors, the analysis uses a factorization method.
That made possible the factorization of Jacobian for networks of several hundreds of nodes and in turn the use of the Newton method.
Many computational tasks, such as decodings or the factorization of very large numbers, would become feasible that are infeasible with present machines.
To exploit this, a common approach is to factorize the operator once and apply the factorization to the following steps.

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