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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

## Coprime Number Finder

### 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/relatively primes.

### 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 (pairwise).

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 coprime as 4 and 6 are not relatively primes.

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

### How to prove that 2 numbers are coprimes?

For two numbers a and b, Calculate the GCD(a,b) of the 2 numbers, if it is equal to 1 then the 2 numbers a and b are relatively primes.

### 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.

### How to check coprime numbers with a calculator?

Some calculators have the coprime() function or use the gcd() function and check that the value is 1.

### 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.

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Coprimes on dCode.fr [online website], retrieved on 2024-09-14, https://www.dcode.fr/coprimes

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