Coprime Lattice of 4 and 9 Coffee Mug

This lattice illustrates that the integers 4 and 9 are coprime if and only if the point with coordinates (4, 9) in a Cartesian coordinate system is "visible" from the origin (0,0), in the sense that there is no point with integer coordinates between the origin and (4, 9). In mathematics, two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1. For example, 6 and 35 are coprime, but 6 and 27 are not coprime because they are both divisible by 3. The number 1 is coprime to every integer. A fast way to determine whether two numbers are coprime is given by the Euclidean algorithm. Euler's totient function (or Euler's phi function) of a positive integer n is the number of integers between 1 and n which are coprime to n.