ABSTRACT

Number theory is, simply put, the theory of numbers. It is where mathematics began, and it holds some of the simplest yet most difficult unsolved problems in the field. Number theory is often concerned with factors of positive integers. A positive integer’s multiples are the integers that it is a factor of. Since there are infinite positive integers, every integer has an infinite number of multiples. Prime numbers are positive integers with no factors except one and themselves. Composite numbers are positive integers that are not prime. The prime factorization of a number contains a lot of information about the number, and it also serves as a unique identification tag. All factors of a number are subsets of its prime factorization. Therefore, one can tell if a number is divisible by another based on their prime factorizations—it is divisible if the quotient of their prime factorizations yield an integral result.