In a unique factorization domain, any two elements have a least common multiple.
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The class of unique factorization domains is related to other classes of rings.
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A factorization system for a category also gives rise to a notion of embedding.
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It contains several factorization methods like Elliptic Curve Method and MPQS.
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Squarity testing can be used as alternative way in factorization of large numbers.
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In these more general environments you cannot take prime factorization for granted.
From the scienceblogs.com
Many authors assume 1 to be a natural number that has no prime factorization.
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For example, in polynomial factorization, they may refer to the input degree.
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Integer factorization is often confused with the closely related primality problem.
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More examples
(mathematics) the resolution of an entity into factors such that when multiplied together they give the original entity
(factorize) resolve (a polynomial) into factors
: The process of creating a list of factors; : An expression listing items that, when multiplied together, will produce a desired quantity; A list of factors