# Thread: Greatest Common Divisor of (9m+8, 6m+5)

1. ## Greatest Common Divisor of (9m+8, 6m+5)

I have a task where I need to calculate the greatest common divisor of (9m+8, 6m+5)
for all m (m is an integer).

It would seem that the answer is 1, but I need a sufficient way to prove it. I already know that gcd(a+kb, b) = gcd(a,b) , so gcd(9m+8, 9) = gcd(6m+5, 6) = 1. However, I'm unsure of how to apply this.

Any help would be greatly appreciated.

2. Originally Posted by Koaske
I have a task where I need to calculate the greatest common divisor of (9m+8, 6m+5)
for all m (m is an integer).

It would seem that the answer is 1, but I need a sufficient way to prove it. I already know that gcd(a+kb, b) = gcd(a,b) , so gcd(9m+8, 9) = gcd(6m+5, 6) = 1. However, I'm unsure of how to apply this.

Any help would be greatly appreciated.
(9m+8, 6m+5)=(3m+3, 6m+5)=(3m+3, 3m+2)=1