What is Turing Machine EUC?

Turing Machine EUC is one of the example Turing Machines that Sir Roger Penrose described on page 54 of his book The Emperor's New Mind (Oxford University Press, 1989).

It is also one of the sample Turing Machines that's built into both of the Excel files that you can download from the Home page of this website.

What the EUC Turing Machine does is read two numbers from the tape (both in Unary Notation), apply the Euclidean Algorithm to compute their Greatest Common Divisor, and display the answer on the tape (again in Unary Notation).

In his book The Emperor's New Mind, Penrose calls the result of the Euclidean Algorithm the Greatest Common Factor rather than the Greatest Common Divisor, but it's the same thing.