I have noticed that calculating the GCD of two odd numbers or an odd number and an even number always equals 1 to me. However, it is of course impossible for me try this out on all uneven numbers and I would like to know if someone knows of a proof or something alike out there that shows this is true for every case with two odd numbers and an odd number and an even number.
BTW, I already have done some research, can't seem to find anything. But thanks in forward if anyone has something.
EDIT: Ok, so since the gcd of the two odd numbers 9 and 15 is 3 I now know that it is not always the case that the gcd is 1 for two odd numbers. However, is there in some way a method to do the gcd of two numbers and already being sure before doing the calculation that it equals 1? Or is it just something you have to try a couple of times on different numbers knowing that odd numbers often have a GCD of 1 until you find gcd=1?