What does factorable mean?
Factorable is an adjective describing something that can be broken down into factors — most commonly a polynomial or integer that can be written as a product of two or more simpler expressions. In algebra, recognizing that x² − 9 is factorable as (x + 3)(x − 3) is a foundational skill, and the term appears constantly in classrooms, textbooks, and problem sets: students are asked to determine whether an expression is factorable before choosing a solution strategy. By extension, the word can describe any system, task, or quantity that lends itself to decomposition into manageable parts, though this broader use is comparatively rare and retains a technical flavor. The opposite of factorable in arithmetic is prime — a number that resists all such breakdown. Derived from the noun factor via the suffix -able, the word carries a neutral, analytical connotation rather than an emotional one. It is standard in both British and American English, with British writers sometimes preferring the related verb factorise over factorize.
adjectiveCapable of being factored, especially capable of being expressed as a product of simpler polynomials or integers; more generally, able to be broken down into constituent parts.
- (of a polynomial or integer) able to be expressed as a product of two or more nontrivial factors.
- (more generally) able to be divided into or analyzed in terms of component parts.
"The quadratic proved factorable once the students spotted its common factor."
"Because x² − 9 is factorable, it can be written as (x + 3)(x − 3)."
"The committee found the problem so complex that no part of it seemed readily factorable into independent tasks."
Every whole number greater than one is either prime or factorable — meaning 'factorable' is essentially the mathematical word for 'interesting.'
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of factorable
Factorable derives from the noun factor, which English borrowed from French in the late Middle Ages; the French word traces to Latin factor, meaning 'a doer or maker,' from facere, 'to do or make.' The adjective was formed with the suffix -able, indicating capacity, likely during the development of modern algebraic terminology in early modern Europe. It shares this Latin root with words such as factory, faction, and fiction-adjacent formations like factitious.
Related word forms
How factorable is actually used
Primarily used in mathematics education and technical writing; outside mathematics it appears rarely and sounds somewhat technical. In number theory, an integer that is not factorable (other than trivially by 1 and itself) is called prime.
Easily confused with factorable
A fractal is a self-similar geometric shape, whereas something factorable can be broken down into multiplicative components.
Factual means based on facts, while factorable refers to being decomposable into factors.