factorize
C2Formal, Technical
Definition
Meaning
To break down a number into its constituent factors; to express an algebraic expression as a product of its factors.
In mathematics, to decompose an object (number, polynomial, matrix) into a product of simpler or irreducible objects. In broader contexts, sometimes used metaphorically to mean analysing something into its basic components.
Linguistics
Semantic Notes
Primarily a mathematical term. In UK English, 'factorise' (with an 's') is the standard spelling, while 'factorize' (with a 'z') is more common in US English. The term implies a specific, rule-based decomposition, not just any breakdown.
Dialectal Variation
British vs American Usage
Differences
Spelling: UK 'factorise' vs US 'factorize'. The mathematical concept is identical, and the term is not widely used outside mathematical/technical contexts, so dialectal usage differences are minimal.
Connotations
In both dialects, the word is neutral, carrying a precise technical meaning without significant positive or negative associations.
Frequency
Usage frequency is comparable in both dialects, limited almost exclusively to mathematical, scientific, and educational contexts.
Vocabulary
Collocations
Grammar
Valency Patterns
[verb] + [noun phrase: number/expression][verb] + [noun phrase] + [prepositional phrase: into factors]Vocabulary
Synonyms
Strong
Neutral
Weak
Vocabulary
Antonyms
Phrases
Idioms & Phrases
- “No common idioms”
Usage
Context Usage
Business
Virtually never used in standard business contexts.
Academic
Used in mathematics textbooks, exams, and lectures, especially in algebra and number theory.
Everyday
Extremely rare; would only be used when discussing homework or a specific mathematical problem.
Technical
Core term in mathematics, computer algebra systems, and cryptography (e.g., factorizing large numbers).
Examples
By Part of Speech
verb
British English
- The student was asked to factorise the quadratic equation.
- Can you factorise 36 into its prime factors?
- We will learn to factorise expressions with a common term.
American English
- The first step is to factorize the polynomial completely.
- The algorithm can factorize very large integers.
- She taught us how to factorize by grouping.
adverb
British English
- He worked factorisingly through the list of equations. (Note: Extremely rare and non-standard; included for structure completeness)
American English
- The expression was factorizably simple. (Note: Extremely rare and non-standard; included for structure completeness)
adjective
British English
- The factorisable expression was simplified quickly. (Note: 'factorisable' is the derived adjective)
- Prime numbers are not factorisable.
American English
- The factorizable matrix revealed its eigenvalues. (Note: 'factorizable' is the derived adjective)
- Not all polynomials are easily factorizable.
Examples
By CEFR Level
- This is a simple number to factorise. (UK)
- Let's factorize this small number. (US)
- In maths class today, we learned how to factorise basic polynomials. (UK)
- You must factorize the expression before you can solve for x. (US)
- The ability to factorise complex algebraic expressions is crucial for calculus. (UK)
- Cryptography relies on the difficulty of factorizing the product of two large prime numbers. (US)
- The theorem provides a method to factorise any polynomial over the complex numbers. (UK)
- Advanced algorithms are constantly being developed to factorize integers more efficiently. (US)
Learning
Memory Aids
Mnemonic
Think of a factory (sounds like 'factor-ize') that takes a complex product and breaks it down into the basic parts (factors) it was made from.
Conceptual Metaphor
MATHEMATICAL DECOMPOSITION IS DISASSEMBLY.
Watch out
Common Pitfalls
Translation Traps (for Russian speakers)
- Do not confuse with 'factor' as a business agent or cause ('фактор'). The mathematical meaning corresponds to 'разложить на множители'.
- Avoid using it as a general synonym for 'analyse' ('анализировать').
Common Mistakes
- Using 'factorize' to mean simply 'analyse' in non-mathematical contexts (e.g., 'We need to factorize the market data').
- Confusing spelling: using 'factorise' in a US context or 'factorize' in a strict UK context.
- Using it intransitively (e.g., 'The number factorizes' is acceptable in maths, but 'We need to factorize' is incomplete without an object).
Practice
Quiz
In which context is the word 'factorize' most appropriately used?
FAQ
Frequently Asked Questions
'Factorize' specifically means to express as a product of factors. 'Simplify' is broader and can mean reducing an expression to a simpler form, which may involve factoring, but also combining like terms or cancelling.
Yes, almost exclusively. While it can be used metaphorically in very technical writing (e.g., 'factorize a problem'), this is rare. In everyday language, 'analyse' or 'break down' are preferred.
The process or result is 'factorization' (US) or 'factorisation' (UK).
No, by definition, a prime number has only two distinct positive factors: 1 and itself. Therefore, it cannot be broken down into a product of smaller integers (other than 1 x itself, which is trivial and not considered proper factorization).