The mathematical quality of being able to be broken down into factors; the degree to which a number or expression can be separated into its component parts.
From 'factorable' (able to be factored) plus '-ity' (state or quality). A technical mathematics term formed following standard word-building patterns for discussing mathematical properties.
Mathematicians obsess over factorability because it's the gateway to solving equations. A number's factorability determines whether a seemingly impossible problem becomes straightforward—it's why primes are so special and valuable in cryptography.
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