The GCD of given numbers is 11.
Step 1 :
Divide $ 2189 $ by $ 121 $ and get the remainder
The remainder is positive ($ 11 > 0 $), so we will continue with division.
Step 2 :
Divide $ 121 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.
We can summarize an algorithm into a following table.
2189 | : | 121 | = | 18 | remainder ( 11 ) | ||
121 | : | 11 | = | 11 | remainder ( 0 ) | ||
GCD = 11 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.