This research focuses on two types of finite abelian groups: the group of integers under addition modulo $n$, and the group of integers under multiplication modulo $n$, where $n$ is any positive integer up to 300. The computations in this study revolve around various properties of these groups, including the order of the group, the order and inverse of each element, the identification of cyclic subgroups, and the determination of generators within the group. To facilitate these calculations, a specialized program was developed using MATLAB. With this program, users can obtain answers for the aforementioned properties of these groups for any integer ranging from 0 to 300.