The GCD of given numbers is 1.
Step 1 :
Divide $ 621 $ by $ 259 $ and get the remainder
The remainder is positive ($ 103 > 0 $), so we will continue with division.
Step 2 :
Divide $ 259 $ by $ \color{blue}{ 103 } $ and get the remainder
The remainder is still positive ($ 53 > 0 $), so we will continue with division.
Step 3 :
Divide $ 103 $ by $ \color{blue}{ 53 } $ and get the remainder
The remainder is still positive ($ 50 > 0 $), so we will continue with division.
Step 4 :
Divide $ 53 $ by $ \color{blue}{ 50 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 50 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 2 $ 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.
621 | : | 259 | = | 2 | remainder ( 103 ) | ||||||||||||
259 | : | 103 | = | 2 | remainder ( 53 ) | ||||||||||||
103 | : | 53 | = | 1 | remainder ( 50 ) | ||||||||||||
53 | : | 50 | = | 1 | remainder ( 3 ) | ||||||||||||
50 | : | 3 | = | 16 | remainder ( 2 ) | ||||||||||||
3 | : | 2 | = | 1 | remainder ( 1 ) | ||||||||||||
2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.