The mathematical process or result of breaking down a number or expression into its factors; the representation of something as a product of factors.
From 'factorize' (to break into factors) plus '-tion' (noun suffix marking an action). A technical mathematical term developed as algebraic notation advanced in the 18th-19th centuries.
Prime factorization—finding the unique set of primes that multiply to make a number—is so important that it's literally impossible (with current technology) to factorize very large numbers. This 'hardness' is what keeps your bank passwords safe.
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