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In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1.[1] Consequently, any prime number that divides a does not divide b, and vice versa. This is equivalent to their greatest common divisor (GCD) being 1.[2] One says also a is prime to b or a is coprime with b.
The numbers 8 and 9 are coprime, despite the fact that neither—considered individually—is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition.
- ^ Eaton, James S. (1872). A Treatise on Arithmetic. Boston: Thompson, Bigelow & Brown. p. 49. Retrieved 10 January 2022.
Two numbers are mutually prime when no whole number but one will divide each of them
- ^ Hardy & Wright 2008, p. 6