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Coprimes

Tool to test / find / check co-prime numbers (relatively prime). Two (or more) Integers are called coprimes if their GCD (greatest common divisor) is equal to 1.

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Coprimes -

Tag(s) : Arithmetics

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# Coprimes

## Answers to Questions (FAQ)

### What are coprimes/relatively primes numbers? (Definition)

Relatively prime numbers (coprimes) are numbers that share no common divisor (except 1).

Example: The number 4 has 1, 2 and 4 as divisors
The number 9 has 1, 3 and 9 as divisors
Numbers 4 and 9 share the number 1 as the only common divisor and so are coprimes.

### How to calculate if numbers are coprimes?

Formally, in mathematics, two numbers are coprimes if the GCD (greatest common divisor) of these numbers is equal to 1. This definition can be extended to N numbers.

Example: GCD(4,6) = 2, then 4 and 6 are not coprimes.

Example: GCD (4,5,6) = 1 then 4, 5 and 6 are coprimes, but not pairwise comprime as 4 and 6 are not relatively primes.

Example: GCD (7,12) = 1 then 7 and 12 are coprimes.

### How to find a coprime number with another?

dCode's calculator/checker tests numbers depending on the prime factor decomposition of the first number (and therefore its divisors) to find coprime numbers. Then check that GCD equals 1 to confirm the number.

See also the Euler Totient or the primality tests.

### Are 1 and 1 coprimes?

According to the definition, yes, 1 and 1 are coprimes as GCD(1,1)=1. Moreover 1 and any positive integer are relatively primes.

## Source code

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Coprimes on dCode.fr [online website], retrieved on 2022-09-29, https://www.dcode.fr/coprimes

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## Questions / Comments

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