The GCD of given numbers is 1.
Step 1 :
Divide $ 6897 $ by $ 1597 $ and get the remainder
The remainder is positive ($ 509 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1597 $ by $ \color{blue}{ 509 } $ and get the remainder
The remainder is still positive ($ 70 > 0 $), so we will continue with division.
Step 3 :
Divide $ 509 $ by $ \color{blue}{ 70 } $ and get the remainder
The remainder is still positive ($ 19 > 0 $), so we will continue with division.
Step 4 :
Divide $ 70 $ by $ \color{blue}{ 19 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 5 :
Divide $ 19 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 6 :
Divide $ 13 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 6 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
6897 | : | 1597 | = | 4 | remainder ( 509 ) | ||||||||||||
1597 | : | 509 | = | 3 | remainder ( 70 ) | ||||||||||||
509 | : | 70 | = | 7 | remainder ( 19 ) | ||||||||||||
70 | : | 19 | = | 3 | remainder ( 13 ) | ||||||||||||
19 | : | 13 | = | 1 | remainder ( 6 ) | ||||||||||||
13 | : | 6 | = | 2 | remainder ( 1 ) | ||||||||||||
6 | : | 1 | = | 6 | remainder ( 0 ) | ||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.