The theory of numbers is a branch of mathematics that focuses on the properties and relationships of numbers, particularly integers. It explores concepts such as divisibility, prime numbers, and congruences, providing a foundation for understanding how numbers interact with one another. One of the key areas within the theory of numbers is prime factorization, which involves breaking down a number into its prime components. This field also includes famous problems and theorems, such as Fermat's Last Theorem and the Goldbach Conjecture, which have intrigued mathematicians for centuries.