This means that the \(\gcd\left(89,144\right)=1.\) Notice from the Euclidean Algorithm above that every remainder we have for each equation represents a Fibonacci number and going from bottom to top, we have generated the Fibonacci Sequence. This will occur when we are trying to find the greatest common divisor of two consecutive Fibonacci numbers. With that in mind, we can also repeat this process for nonconsecutive Fibonacci numbers. In either case, the last nonzero remainder produced will always result in a solution that is also a Fibonacci number. 
To generalize conversion, we can take any two Fibonacci numbers, \(F_{n+1}\) and \(F_n\). Their ratio is: