In a principal ideal domain, this operation corresponds to finding the generator of the ideal generated by two elements.
The natural numbers form a complete distributive lattice with this operation corresponding to meet. In a principal ideal domain, this operation corresponds to finding the generator of the ideal generated by two elements. For integers x and y, this is the smallest positive integer that can be written as "a-x plus b-y", according to Bezout's identity. Performing this operation on two integers is equivalent to performing it on the smaller of the two integers and the (*) difference between them. That fact is the basis for the Euclidean algorithm, which computes this quantity more efficiently than first computing the prime factorization of both inputs. For a natural number n and zero, this value is n, while for two relatively prime numbers, this value is one. For 10 points, name this value which is the largest positive integer that divides two given numbers.
The natural numbers form a complete distributive lattice with this operation corresponding to meet.
greatest common divisor [or GCD; or greatest common factor; or highest common factor; or GCF; or HCF]