The GCD of given numbers is 1.
Step 1 :
Divide $ 2689 $ by $ 1369 $ and get the remainder
The remainder is positive ($ 1320 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1369 $ by $ \color{blue}{ 1320 } $ and get the remainder
The remainder is still positive ($ 49 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1320 $ by $ \color{blue}{ 49 } $ and get the remainder
The remainder is still positive ($ 46 > 0 $), so we will continue with division.
Step 4 :
Divide $ 49 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 46 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
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.
2689 | : | 1369 | = | 1 | remainder ( 1320 ) | ||||||||||
1369 | : | 1320 | = | 1 | remainder ( 49 ) | ||||||||||
1320 | : | 49 | = | 26 | remainder ( 46 ) | ||||||||||
49 | : | 46 | = | 1 | remainder ( 3 ) | ||||||||||
46 | : | 3 | = | 15 | 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.