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  The extended Euclidean algorithm is an algorithm used to calculate the greatest common divisor (gcd, or also highest common factor, HCF) of two integers a and b, as well as integers x and y such that 
  To illustrate the extension of the Euclid’s algorithm, consider the computation of gcd(120, 23), which is shown on the table on the left. 
  This method attempts to solve the required equation with the sum replaced by the remainders in each step of the algorithm, which is larger than their gcd, but are decreasing in magnitude, and so will eventually become the required equation. 
 random.dragonslife.org /extendedeuclideanalgorithm/4414 (0 words) 
