This research is an exposition on the topic Divisibility Criteria which are the bases of the different Divisibility Rules. It is a detailed study based on the discussion on Divisibility Criteria in the book Number Theory by Sergio Ymas, with the goal of arriving at a fixed rule or test mathematically formulated as:

n a_k+a_(k+1) (mod m)

when dealing with divisibility by m where m is prime.In particular, this paper aims to show in greater detail how the easier rules on divisibility by prime numbers are obtained. This paper also aims to justify that the existing rules on divisibility by 7 and 13 are not merely obtained by trial and error but instead existing rules are based on Number Theory. Finally, this study aims to justify the existence of fixed and efficient tests for divisibility by prime numbers higher than or equal to 17.