The GCD of given numbers is 1.
Step 1 :
Divide $ 5723 $ by $ 5036 $ and get the remainder
The remainder is positive ($ 687 > 0 $), so we will continue with division.
Step 2 :
Divide $ 5036 $ by $ \color{blue}{ 687 } $ and get the remainder
The remainder is still positive ($ 227 > 0 $), so we will continue with division.
Step 3 :
Divide $ 687 $ by $ \color{blue}{ 227 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 227 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 5 :
Divide $ 6 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
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.
5723 | : | 5036 | = | 1 | remainder ( 687 ) | ||||||||||
5036 | : | 687 | = | 7 | remainder ( 227 ) | ||||||||||
687 | : | 227 | = | 3 | remainder ( 6 ) | ||||||||||
227 | : | 6 | = | 37 | remainder ( 5 ) | ||||||||||
6 | : | 5 | = | 1 | 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.