In mathematics, two integers (a and b) are co-prime (or relatively prime) if they share no common factors. This is sometimes written as .[1][2] In other words, there is no number, other than 1, that divides both a and b evenly.[3] In which case, the greatest common divisor (GCD, or highest common factor) of these numbers is 1.[2]
As an example, 6 and 35 are coprime, because the factors of 6, 2 and 3, do not divide 35 evenly. On the other hand, 6 and 27 are not coprime, because 3 divides both 6 and 27. Another example is 4 and 5: 4 = 2*2*1; 5 = 5*1 (Prime). The only common factor is 1, so they are coprime.
On the other hand, 10 and 5: 10 = 5*2 5 = 5*1 (Prime). The common factors are 5 and 1, so they are not coprime.
Prime numbers are always coprime to each other.
- Any two consecutive integers are always coprime.
- Sum of any two coprime numbers is always coprime to their product.
- 1 is trivially coprime with all numbers.
- if out of two numbers, any one number is a prime number while the other number is not a multiple of first one, then both are coprime.
- This is not applicable to negative numbers
Related pages
References
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