The GCD of given numbers is 13.
Step 1 :
Divide $ 117 $ by $ 65 $ and get the remainder
The remainder is positive ($ 52 > 0 $), so we will continue with division.
Step 2 :
Divide $ 65 $ by $ \color{blue}{ 52 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 3 :
Divide $ 52 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 13 }} $.
We can summarize an algorithm into a following table.
117 | : | 65 | = | 1 | remainder ( 52 ) | ||||
65 | : | 52 | = | 1 | remainder ( 13 ) | ||||
52 | : | 13 | = | 4 | remainder ( 0 ) | ||||
GCD = 13 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.