How this calculator works
Two integers are relatively prime, or coprime, when their only common positive factor is 1. For a whole set the test is weaker: the set is relatively prime when the greatest common factor of all its members is 1. Pairwise coprime is stricter, requiring every individual pair to be coprime. The set 6, 10 and 15 shows the difference: no single factor divides all three, yet 6 and 10 share 2, so the set is relatively prime but not pairwise coprime.
Formula
A set is relatively prime when gcd(a₁, a₂, ..., aₙ) = 1. It is pairwise coprime when gcd(aᵢ, aⱼ) = 1 for every i ≠ j. The gcd is computed with Euclid's algorithm.
Worked example
12 and 25 are relatively prime because their factors are {1, 2, 3, 4, 6, 12} and {1, 5, 25}, which meet only at 1. The numbers 12 and 18 are not: they share the factor 6.
Advertisement
Frequently asked questions
Does 1 count as relatively prime to anything?
Yes. The only positive factor of 1 is 1, so gcd(1, n) = 1 for every integer n. A set containing 1 is therefore always relatively prime.
Are relatively prime numbers always prime?
No. The name describes the relationship, not the numbers. 8 and 9 are both composite, but they share no factor other than 1, so they are relatively prime.
How is pairwise coprime different?
A set can have gcd 1 without every pair being coprime, as with 6, 10 and 15. Pairwise coprime rules out even that: every two members must be coprime. For two numbers the two tests agree.
What happens with negative numbers?
Signs are ignored. The greatest common factor is defined on absolute values, so -12 and 25 are relatively prime in exactly the same way as 12 and 25.