Before moving on, trace GCD(, ) by hand. Write down each recursive call and the values of and . Start: GCD(, ). What is ? That becomes the new .
What is the new ? Keep going until you hit the base case. Check your answer: the sequence should be GCD(, ) → GCD(, ) → GCD(, ) → GCD(, ). The answer is . If you got this right, you understand how GCD shrinks toward the base case. If not, re-read the GCD units.