Euclid’s Algorithm

Abstract

Among the mathematical problems we will investigate are computing greatest common divisors, factoring into prime factors and finding rational approximations. These computations may be performed on a variety of different mathematical quantities: polynomials, rational integers, power series, differential operators, etc. The most familiar of these algebraic structures are the natural numbers: ℕ={1,2,3,...}. If we include zero and the negative integers we have ℤ, the rational integers, which are commonly called the integers.