The GCD of given numbers is 1.
Step 1 :
Divide $ 236 $ by $ 129 $ and get the remainder
The remainder is positive ($ 107 > 0 $), so we will continue with division.
Step 2 :
Divide $ 129 $ by $ \color{blue}{ 107 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 3 :
Divide $ 107 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 19 > 0 $), so we will continue with division.
Step 4 :
Divide $ 22 $ by $ \color{blue}{ 19 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 19 $ 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.
236 | : | 129 | = | 1 | remainder ( 107 ) | ||||||||||
129 | : | 107 | = | 1 | remainder ( 22 ) | ||||||||||
107 | : | 22 | = | 4 | remainder ( 19 ) | ||||||||||
22 | : | 19 | = | 1 | remainder ( 3 ) | ||||||||||
19 | : | 3 | = | 6 | 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.