, so we start checking
all the numbers from a down to 1 to see if any divide both numbers.
Whichever one does is the greatest (because we are working our way
down) common divisor.
Step 2, correctness is relatively easy. It follows from the
definition. We know the , so we start checking
all the numbers from a down to 1 to see if any divide both numbers.
Whichever one does is the greatest (because we are working our way
down) common divisor.
Why does it terminate? Because 1 divides everything.
Step 3 (efficiency analysis) is much more subtle. Unlike multiplication, it doesn't grow steadily with a. The number of recursive calls could be anywhere between 1 and a!
