The GCD of given numbers is 97.
Step 1 :
Divide $ 1649 $ by $ 97 $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 97 }} $.
We can summarize an algorithm into a following table.
1649 | : | 97 | = | 17 | remainder ( 0 ) |
GCD = 97 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.