relatively prime numbers: meaning, definition, pronunciation and examples
C1Technical/Formal
Quick answer
What does “relatively prime numbers” mean?
Two or more integers that share no common positive divisor other than 1.
Audio
Pronunciation
Definition
Meaning and Definition
Two or more integers that share no common positive divisor other than 1.
A set of numbers whose greatest common divisor (GCD) is 1; used in number theory, cryptography, and algorithm design.
Dialectal Variation
British vs American Usage
Differences
No significant differences in meaning. 'Coprime' is slightly more common in British technical writing, while 'relatively prime' is standard in both.
Connotations
Purely mathematical, no cultural connotations.
Frequency
Exclusively used in mathematical, computer science, and engineering contexts.
Grammar
How to Use “relatively prime numbers” in a Sentence
Number A and number B are relatively prime.The numbers [list] are relatively prime.Two integers are relatively prime if their GCD is 1.Vocabulary
Collocations
Examples
Examples of “relatively prime numbers” in a Sentence
adjective
British English
- The two numbers are coprime.
- We need a set of coprime integers.
American English
- The two numbers are relatively prime.
- We need a set of relatively prime integers.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Core concept in undergraduate number theory, abstract algebra, and cryptography courses.
Everyday
Extremely rare outside of specific educational or puzzle contexts.
Technical
Essential in algorithm design (e.g., RSA encryption), hash functions, and random number generation.
Vocabulary
Synonyms of “relatively prime numbers”
Strong
Neutral
Weak
Vocabulary
Antonyms of “relatively prime numbers”
Watch out
Common Mistakes When Using “relatively prime numbers”
- Saying 'a relatively prime number' (it's a relational property, needs at least two numbers).
- Confusing with 'prime numbers' (all primes are coprime to each other, but numbers like 8 and 9 are coprime without being prime).
FAQ
Frequently Asked Questions
Yes, any two distinct prime numbers are always relatively prime, as their only common divisor is 1.
Absolutely. Example: 9 (3x3) and 10 (2x5) are composite and relatively prime because they share no common factors.
'Prime' describes a single number divisible only by 1 and itself. 'Relatively prime' describes a relationship between two or more numbers that share no common factors other than 1.
Because the security of algorithms like RSA depends on the difficulty of factoring the product of two large, relatively prime numbers.
Two or more integers that share no common positive divisor other than 1.
Relatively prime numbers is usually technical/formal in register.
Relatively prime numbers: in British English it is pronounced /ˌrɛl.ə.tɪv.li ˈpraɪm ˈnʌm.bəz/, and in American English it is pronounced /ˌrɛl.ə.t̬ɪv.li ˈpraɪm ˈnʌm.bɚz/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “Share nothing but one”
Learning
Memory Aids
Mnemonic
Think of two neighbours who share only one fence post (the number 1). They are otherwise independent.
Conceptual Metaphor
Mathematical siblings with no common inheritance (besides the universal '1').
Practice
Quiz
Which pair is relatively prime?