Euclidean algorithm, procedure for finding the greatest common divisor (GCD) of two numbers, described by the Greek mathematician Euclid in his Elements (c. 300 bc). The method is computationally efficient and, with minor modifications, is still used by
The above algorithm is not optimal for this example because it performs many comparisons (starting from 540, decrementing by 1 for each iteration down to 60) to find the actual solution. So, the iteration keeps going (540, 539, 538, ..., 60) until we get 60. There is another approach...
Algorithm and bound for the greatest common divisor of n integers A new version of the Euclidean algorithm for finding the greatest common divisor of n integers ai and multipliers xi such that gcd = x1 a1 + ··· + xn an... GH Bradley - 《Communications of the Acm》 被引量: 99发表...
How to Use Euclid’s Algorithm to Find the Greatest Common Factor Euclid’s algorithm defines the technique for finding the greatest common factor of two numbers. The greatest common factor (GCF), also referred to as the greatest common divisor (GCD), is the largest whole number that divides...
A carry-free algorithm for finding the greatest common divisor of two integers We investigate a variant of the so-called "binary" algorithm for finding the GCD (greatest common divisor) of two numbers which requires no comparisons. We show that when implemented with carry-save hardware, it can...