The GCD of given numbers is 1.
Step 1 :
Divide $ 2165 $ by $ 1287 $ and get the remainder
The remainder is positive ($ 878 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1287 $ by $ \color{blue}{ 878 } $ and get the remainder
The remainder is still positive ($ 409 > 0 $), so we will continue with division.
Step 3 :
Divide $ 878 $ by $ \color{blue}{ 409 } $ and get the remainder
The remainder is still positive ($ 60 > 0 $), so we will continue with division.
Step 4 :
Divide $ 409 $ by $ \color{blue}{ 60 } $ and get the remainder
The remainder is still positive ($ 49 > 0 $), so we will continue with division.
Step 5 :
Divide $ 60 $ by $ \color{blue}{ 49 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 6 :
Divide $ 49 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 7 :
Divide $ 11 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 5 $ 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.
2165 | : | 1287 | = | 1 | remainder ( 878 ) | ||||||||||||||
1287 | : | 878 | = | 1 | remainder ( 409 ) | ||||||||||||||
878 | : | 409 | = | 2 | remainder ( 60 ) | ||||||||||||||
409 | : | 60 | = | 6 | remainder ( 49 ) | ||||||||||||||
60 | : | 49 | = | 1 | remainder ( 11 ) | ||||||||||||||
49 | : | 11 | = | 4 | remainder ( 5 ) | ||||||||||||||
11 | : | 5 | = | 2 | remainder ( 1 ) | ||||||||||||||
5 | : | 1 | = | 5 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.