What does factorize mean?
Factorize is a verb used chiefly in mathematics to describe the process of expressing a number, polynomial, or other expression as a product of its factors. For example, the number 12 can be factorized as 2 × 2 × 3, and the quadratic expression x² − 5x + 6 can be factorized as (x − 2)(x − 3). This operation is fundamental across algebra and number theory because it often simplifies equations, reveals structure, and enables solutions that would otherwise be difficult to obtain. Beyond mathematics, factorize can also mean breaking down any complex thing—such as a process or problem—into simpler components, though this broader sense is less frequent. Related forms include the noun factorization and the adjective factorizable. Because factoring large numbers is computationally hard, factorize also carries significance in cryptography, where the security of certain systems depends on how difficult it is to factorize very large integers.
verbTo express a number, polynomial, or other mathematical expression as a product of factors; more broadly, to break something down into its constituent parts or elements.
- (Mathematics) To express a number or algebraic expression as a product of two or more factors.
- More generally: to decompose or break down something (such as a problem, process, or system) into simpler constituent parts.
"To solve the quadratic equation, first factorize the expression on the left-hand side."
"Students learn to factorize expressions like x² − 5x + 6 as part of introductory algebra."
"The engineer factorized the complex workflow into discrete, testable stages."
Every whole number greater than 1 has exactly one way to be factorized into primes — a fact so fundamental it's called the fundamental theorem of arithmetic.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of factorize
Factorize derives from the noun "factor," which entered English in the late Middle Ages from Latin "factor," meaning "a doer or maker," itself from the past participle of "facere" ("to do or make"). The verb factorize was formed later by adding the suffix -ize, which marks verbs meaning "to make into or treat as." It shares this Latin root with words such as factory, faction, and manufacture, all ultimately tracing back to facere.
Related word forms
How factorize is actually used
In American English, the spelling "factorize" is common alongside the variant "factorize"/"factorize" — note that "factorize" with -ize is standard in both varieties, though British texts sometimes prefer "factorise". The word is primarily technical, appearing most often in mathematical and scientific contexts. In everyday speech outside mathematics, "break down" or "decompose" are usually preferred.
Easily confused with factorize
"Fracture" means to break or crack something physically, while "factorize" is the mathematical process of expressing something as a product of factors.