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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.
This kind of factorization keeps matrix entries based on the matrix adjacency graph.
Every factorization of n that contains an odd factor will give exactly one trapezoidal representation.
We also want to study block ILUT factorization.
The work of art stood as the last bastion of pure form perceived as a whole, rejecting any factorization.
Many computational tasks, such as decodings or the factorization of very large numbers, would become feasible that are infeasible with present machines.

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