Noun
the largest integer that divides without remainder into a set of integers
Source: WordNetIf two numbers have no prime factors in common, their greatest common divisor is 1 (obtained here as an instance of the empty product ), in other words they are coprime. Source: Internet
Footnote 27, p. 9: "For example, the natural numbers with gcd (greatest common divisor) as meet and lcm (least common multiple) as join operation determine a (complete distributive) lattice." Source: Internet
Dividing by their greatest common divisor is a way to improve the running time. Source: Internet
Given two positive integers their least common multiple and greatest common divisor are given by the formulas : and : Since : this gives : In fact, any rational number can be written uniquely as the product of primes if negative exponents are allowed. Source: Internet
In case a denominator and numerator remain that are too large to ensure they are coprime by inspection, a greatest common divisor computation is needed anyway to ensure the fraction is actually irreducible. Source: Internet
Indeed, write x and y as fractions in lowest terms : : where the greatest common divisor of a, b, and c is 1. Then, since x and y are on the unit circle, : and so as claimed. Source: Internet