The GCD of given numbers is 1.
Step 1 :
Divide $ 587 $ by $ 345 $ and get the remainder
The remainder is positive ($ 242 > 0 $), so we will continue with division.
Step 2 :
Divide $ 345 $ by $ \color{blue}{ 242 } $ and get the remainder
The remainder is still positive ($ 103 > 0 $), so we will continue with division.
Step 3 :
Divide $ 242 $ by $ \color{blue}{ 103 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 4 :
Divide $ 103 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 31 > 0 $), so we will continue with division.
Step 5 :
Divide $ 36 $ by $ \color{blue}{ 31 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 6 :
Divide $ 31 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
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.
587 | : | 345 | = | 1 | remainder ( 242 ) | ||||||||||||
345 | : | 242 | = | 1 | remainder ( 103 ) | ||||||||||||
242 | : | 103 | = | 2 | remainder ( 36 ) | ||||||||||||
103 | : | 36 | = | 2 | remainder ( 31 ) | ||||||||||||
36 | : | 31 | = | 1 | remainder ( 5 ) | ||||||||||||
31 | : | 5 | = | 6 | 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.