greatest common divisor: meaning, definition, pronunciation and examples
C1Technical/Academic
Quick answer
What does “greatest common divisor” mean?
The largest positive integer that divides two or more given integers without a remainder.
Audio
Pronunciation
Definition
Meaning and Definition
The largest positive integer that divides two or more given integers without a remainder.
A fundamental concept in number theory representing the largest shared factor of a set of numbers; can be extended metaphorically to represent the most significant shared element or principle in a non-mathematical context.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning or usage. Abbreviation 'GCD' is standard in both. The term 'highest common factor (HCF)' is a synonymous term more commonly taught in British primary/secondary education, while 'greatest common divisor' is dominant in university-level and professional contexts globally.
Connotations
Identical technical connotations.
Frequency
Slightly more frequent in American academic texts, as 'GCD' is the overwhelmingly standard term. In the UK, 'HCF' may appear in earlier educational stages, but 'GCD' is standard in higher education and research.
Grammar
How to Use “greatest common divisor” in a Sentence
The greatest common divisor of [number] and [number] is [number].Find the greatest common divisor for/of [set of numbers].Vocabulary
Collocations
Examples
Examples of “greatest common divisor” in a Sentence
verb
British English
- We need to greatest-common-divisor these values.
- The function greatest-common-divides the inputs.
American English
- The algorithm will greatest-common-divisor the two numbers.
- Let's greatest-common-divide these integers.
adverb
British English
- The numbers divide greatest-common-divisor-ly.
- He calculated it greatest-common-divisor-wise.
American English
- The values were combined greatest-common-divisor-ly.
- It was solved greatest-common-divisor-style.
adjective
British English
- This is the greatest-common-divisor result.
- A greatest-common-divisor approach to the problem.
American English
- The greatest-common-divisor function is key.
- Apply the greatest-common-divisor method.
Usage
Meaning in Context
Business
Rare. Potentially metaphorical: 'Finding the greatest common divisor in the stakeholders' demands was crucial for the agreement.'
Academic
Primary context. Used in mathematics, computer science, and engineering papers and textbooks.
Everyday
Extremely rare, unless discussing math homework.
Technical
Standard term in mathematics, number theory, cryptography, and algorithm design.
Vocabulary
Synonyms of “greatest common divisor”
Strong
Neutral
Weak
Vocabulary
Antonyms of “greatest common divisor”
Watch out
Common Mistakes When Using “greatest common divisor”
- Misspelling 'divisor' as 'diviser' or 'divider'.
- Using 'denominator' instead of 'divisor' (a denominator is specific to fractions).
- Confusing GCD with LCM (Least Common Multiple).
FAQ
Frequently Asked Questions
Yes, for positive integers, 'greatest common divisor (GCD)' and 'highest common factor (HCF)' are completely synonymous terms.
Yes, the GCD is defined for any set of two or more integers. For example, the GCD of 12, 18, and 24 is 6.
By definition, the greatest common divisor of a non-zero integer 'a' and 0 is the absolute value of 'a'. The GCD of 0 and 0 is undefined.
The Euclidean algorithm, attributed to the ancient Greek mathematician Euclid, is a highly efficient method for computing the GCD of two numbers.
The largest positive integer that divides two or more given integers without a remainder.
Greatest common divisor is usually technical/academic in register.
Greatest common divisor: in British English it is pronounced /ˌɡreɪtɪst ˌkɒmən dɪˈvaɪzə/, and in American English it is pronounced /ˌɡreɪtəst ˌkɑːmən dɪˈvaɪzər/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “[Metaphorical] The greatest common divisor of their interests was a love for classical music.”
Learning
Memory Aids
Mnemonic
Think of a pizza shared by friends. The Greatest Common Divisor is the largest slice size you can cut so that everyone gets a whole number of slices without any leftovers.
Conceptual Metaphor
THE CORE SHARED ELEMENT IS THE LARGEST COMMON DIVISOR (e.g., 'The treaty was the greatest common divisor of their conflicting demands.').
Practice
Quiz
What is the greatest common divisor of 36 and 24?