The GCD of given numbers is 1.
Step 1 :
Divide $ 196 $ by $ 55 $ and get the remainder
The remainder is positive ($ 31 > 0 $), so we will continue with division.
Step 2 :
Divide $ 55 $ by $ \color{blue}{ 31 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 3 :
Divide $ 31 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 4 :
Divide $ 24 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 7 $ 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.
196 | : | 55 | = | 3 | remainder ( 31 ) | ||||||||||
55 | : | 31 | = | 1 | remainder ( 24 ) | ||||||||||
31 | : | 24 | = | 1 | remainder ( 7 ) | ||||||||||
24 | : | 7 | = | 3 | remainder ( 3 ) | ||||||||||
7 | : | 3 | = | 2 | 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.