What does factorise mean?
To factorise is to rewrite a number, expression, or equation as a product of simpler components called factors. For example, 18 can be factorised as 2 × 9 or, more fully, as 2 × 3 × 3. In algebra, factorising a polynomial means rewriting it in a form that may make its solutions or structure easier to identify. The verb is especially associated with school and technical mathematics, but it can also be used metaphorically for dividing a complex whole into constituent parts. Its spelling reflects regional convention: factorise is traditional in British English, while factorize is standard in American English. The word is related to multiplication but works in the opposite direction, seeking the elements whose product recreates the original quantity. Consequently, factorisation is valuable whenever a problem is clearer when expressed as a product than as a sum.
verbTo express a number, expression, or equation as a product of simpler factors. It is also used more broadly to mean dividing something into its constituent parts.
- To express a number, expression, or equation as a product of factors, especially prime factors.
"We can factorise 12 as 3 × 4 and 2 × 6."
"The students were asked to factorise the quadratic equation before solving it."
"The programme factorises every incoming expression to make pattern matching easier."
Factorising reverses multiplication: it asks which pieces were multiplied to produce the whole.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does factorise come from?
Factorise was formed in English from factor by adding the verb-forming suffix -ise, a pattern widely used to create verbs from nouns. Factor came into English through Old French from the Latin factor, meaning “doer” or “maker,” which derives from the Latin verb facere, “to make” or “to do.” Related English words include factor, factorial, and factory, although factorise specifically refers to the process of expressing something as a product of factors.
Related word forms
How factorise is actually used
The word is most common in mathematics, algebra, and computing. In British English, factorise is the usual spelling; factorize is the usual American spelling.
Easily confused with factorise
Factorise is the traditional British spelling, while factorize is the standard spelling in American English and is also widely accepted internationally.