The divisibility test is a fascinating topic in number theory. For example, a number is divisible by 2 if and only if it’s last digit is even; a number is divisible by 3 if and only if the sum of all its digits is divisible by 3. In this thesis project, under the guidance of Dr. Han, I will investigate and derive the divisibility criteria for various numbers. I will them investigate possible applications for the gained knowledge of divisibility. To add more depth to this project, I will further investigate various divisibility criteria in different number systems and their applications. The research will be conduced through rigorous mathematical analysis in the area of number theory.