Let "g" = gcd("a", "b"). Since "a" and "b" are both multiples of "g", they can be written "a" = "mg" and "b" = "ng", and there is no larger number "G" > "g" for which this is true. The natural numbers "m" and "n" must be coprime, since any common factor could be factored out of "m" and "n" to make "g" greater. Thus, any other number "c" that divides both "a" and "b" must also divide "g". The greatest common divisor "g" of "a" and "b" is the unique (positive) common divisor of "a" and "b" that is divisible by any other common divisor "c".