The theme of this nal work was the fundamental theorem of arithmetic. In the rst part of the paper, we will get acquainted with the basic structure of numbers that we need to further elaborate the fundamental theorem of arithmetic. Also, we need the notion of divisibility in the set of whole numbers and the prime numbers that we introduce immediately after the division of numbers into the natural and the whole. Then, with the help of prime numbers, we state the fundamental theorem of arithmetic and its proof. The theorem is a very useful result in mathematics. Applies to many areas of the theory of numbers. It is very important in various applications of congruence, as well as in the application of methods for encryption and decryption of messages dealing with scientic discipline cryptography.