The GCD of given numbers is 1.
Step 1 :
Divide $ 11857 $ by $ 6897 $ and get the remainder
The remainder is positive ($ 4960 > 0 $), so we will continue with division.
Step 2 :
Divide $ 6897 $ by $ \color{blue}{ 4960 } $ and get the remainder
The remainder is still positive ($ 1937 > 0 $), so we will continue with division.
Step 3 :
Divide $ 4960 $ by $ \color{blue}{ 1937 } $ and get the remainder
The remainder is still positive ($ 1086 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1937 $ by $ \color{blue}{ 1086 } $ and get the remainder
The remainder is still positive ($ 851 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1086 $ by $ \color{blue}{ 851 } $ and get the remainder
The remainder is still positive ($ 235 > 0 $), so we will continue with division.
Step 6 :
Divide $ 851 $ by $ \color{blue}{ 235 } $ and get the remainder
The remainder is still positive ($ 146 > 0 $), so we will continue with division.
Step 7 :
Divide $ 235 $ by $ \color{blue}{ 146 } $ and get the remainder
The remainder is still positive ($ 89 > 0 $), so we will continue with division.
Step 8 :
Divide $ 146 $ by $ \color{blue}{ 89 } $ and get the remainder
The remainder is still positive ($ 57 > 0 $), so we will continue with division.
Step 9 :
Divide $ 89 $ by $ \color{blue}{ 57 } $ and get the remainder
The remainder is still positive ($ 32 > 0 $), so we will continue with division.
Step 10 :
Divide $ 57 $ by $ \color{blue}{ 32 } $ and get the remainder
The remainder is still positive ($ 25 > 0 $), so we will continue with division.
Step 11 :
Divide $ 32 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 12 :
Divide $ 25 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 13 :
Divide $ 7 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 14 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 15 :
Divide $ 3 $ 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.
11857 | : | 6897 | = | 1 | remainder ( 4960 ) | ||||||||||||||||||||||||||||
6897 | : | 4960 | = | 1 | remainder ( 1937 ) | ||||||||||||||||||||||||||||
4960 | : | 1937 | = | 2 | remainder ( 1086 ) | ||||||||||||||||||||||||||||
1937 | : | 1086 | = | 1 | remainder ( 851 ) | ||||||||||||||||||||||||||||
1086 | : | 851 | = | 1 | remainder ( 235 ) | ||||||||||||||||||||||||||||
851 | : | 235 | = | 3 | remainder ( 146 ) | ||||||||||||||||||||||||||||
235 | : | 146 | = | 1 | remainder ( 89 ) | ||||||||||||||||||||||||||||
146 | : | 89 | = | 1 | remainder ( 57 ) | ||||||||||||||||||||||||||||
89 | : | 57 | = | 1 | remainder ( 32 ) | ||||||||||||||||||||||||||||
57 | : | 32 | = | 1 | remainder ( 25 ) | ||||||||||||||||||||||||||||
32 | : | 25 | = | 1 | remainder ( 7 ) | ||||||||||||||||||||||||||||
25 | : | 7 | = | 3 | remainder ( 4 ) | ||||||||||||||||||||||||||||
7 | : | 4 | = | 1 | remainder ( 3 ) | ||||||||||||||||||||||||||||
4 | : | 3 | = | 1 | remainder ( 1 ) | ||||||||||||||||||||||||||||
3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||||||||||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.