The GCD of given numbers is 19.
Step 1 :
Divide $ 9481 $ by $ 6897 $ and get the remainder
The remainder is positive ($ 2584 > 0 $), so we will continue with division.
Step 2 :
Divide $ 6897 $ by $ \color{blue}{ 2584 } $ and get the remainder
The remainder is still positive ($ 1729 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2584 $ by $ \color{blue}{ 1729 } $ and get the remainder
The remainder is still positive ($ 855 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1729 $ by $ \color{blue}{ 855 } $ and get the remainder
The remainder is still positive ($ 19 > 0 $), so we will continue with division.
Step 5 :
Divide $ 855 $ by $ \color{blue}{ 19 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 19 }} $.
We can summarize an algorithm into a following table.
9481 | : | 6897 | = | 1 | remainder ( 2584 ) | ||||||||
6897 | : | 2584 | = | 2 | remainder ( 1729 ) | ||||||||
2584 | : | 1729 | = | 1 | remainder ( 855 ) | ||||||||
1729 | : | 855 | = | 2 | remainder ( 19 ) | ||||||||
855 | : | 19 | = | 45 | remainder ( 0 ) | ||||||||
GCD = 19 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.