Writing an Extended Euclidean Calculator that calculates the inverse of a modulus can get pretty difficult. However writing a good algorithm and going through step by step can make the process so much easier. So we want to find a’ or inverse of a so that a * a’ [=] 1 (mod b). In other words we are trying to find an integer (a’) when multiplied by a and then divided by b gives you a remainder of 1. In order to find this number(a’), we have to work the Euclidean Algorithm backwards which is referred to as the Extended Euclidean Algorithm.