The Extended Euclidean Algorithm has inputs integers a,b ≥ 1 and outputs integers X,Y such that aX+bY=d=gcd (a,b) is the greatest common divisor of a and b. Starting with A=(1,0,a), B=(0,1,b) the algorithm obtains a sequence of pairs of triples (x,y,z) of integers such that ax+by=z > 0. Given two successive triples A=(x_A,y_A,z_A) and B=(x_B,y_B,z_B) apply the Division Algorithm to the division of z_A by z_B, so that z_A=qz_B+r with quotient q and remainder r such that 0 ≤ r < z_B . The next two triples are then defined by A=B, B=(x_A,y_A,z_A)-q(x_B,y_B,z_B) with the new z_B=z_A-qz_B=r strictly less then the old z_B. The algorithm terminates when the remainder is r=0, returning X=x_B, Y=y_B, d=gcd(a,b)=z_B such that aX+bY=d.

The Javascript Source for the GCD function can be found here.
The function is named gcd(a,b) in file.