The Euclidean Algorithm is a simple means by which the greatest common divisor (GCD) of two positive integers may be found. The Java applet below makes use of the BigInteger class and thus should handle arbitrarily large integers. If you find a case in which the applet fails to function or gives erroneous results, please send me the values of A and B which you entered and the contents of your Java console. My modest goal is to have this applet run reliably and accurately.

The Euclidean Algorithm: Let a and b be integers with a>=b>0 and set r_-1=a, r₀=b. By repeatedly applying the Division Algorithm, we get r_j-1=r_j q_j+1 + r_j+1 with 0 < r_j+1 < r_j for all 0 <=j < n, where n is the least non-negative number such that r_n+1 = 0, in which case gcd(a,b) = r_n.