Number Theory, the investigation of natural numbers, is a time-honored discipline within Mathematics that has captivated mathematicians over numerous centuries due to its inherent purity. In today's world, a thorough understanding of Number Theory is essential for the advancement of cutting-edge technology, as it is extensively applied in domains such as software engineering and cryptography. The objective of this study is to elucidate the understanding of Number Theory that underlies several composite encryption systems and analyze the advantages and disadvantages of each encryption system through a comprehensive examination of existing literature. The discipline of Number Theory has extensive practical implications in cryptography and holds the promise of being increasingly employed in various domains in the future. By elucidating the role of Number Theory in various encryption systems, the fundamental nature of encryption can be enhanced, hence fostering the emergence of novel methodologies or approaches in information security.