Consider the two integers:
\(b = 12121212\)
What is the GCD of \(a\) and \(b\)?
Hint: Looks scary, but it's not.
We run the algorithm:
\[GCD(21212121,12121212)\\ = GCD(12121212,9090909)\\ = GCD(9090909,3030303)\\ = GCD(3030303,0).\]
How many steps of the Euclidean algorithm are needed to compute this GCD?
A step of the Euclidean algorithm is defined as an application of the equation:
\(GCD(x,y) = GCD(y, rem(x, y)).\)
The algorithm begins with \((a,b)\) and ends with \((gcd(a,b),0)\).In the execution of the algorithm in Part 1 we needed 3 applications of the equation.