The GCD of given numbers is 1.
Step 1 :
Divide $ 197 $ by $ 144 $ and get the remainder
The remainder is positive ($ 53 > 0 $), so we will continue with division.
Step 2 :
Divide $ 144 $ by $ \color{blue}{ 53 } $ and get the remainder
The remainder is still positive ($ 38 > 0 $), so we will continue with division.
Step 3 :
Divide $ 53 $ by $ \color{blue}{ 38 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 4 :
Divide $ 38 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 15 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 7 $ 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.
197 | : | 144 | = | 1 | remainder ( 53 ) | ||||||||||||
144 | : | 53 | = | 2 | remainder ( 38 ) | ||||||||||||
53 | : | 38 | = | 1 | remainder ( 15 ) | ||||||||||||
38 | : | 15 | = | 2 | remainder ( 8 ) | ||||||||||||
15 | : | 8 | = | 1 | remainder ( 7 ) | ||||||||||||
8 | : | 7 | = | 1 | remainder ( 1 ) | ||||||||||||
7 | : | 1 | = | 7 | remainder ( 0 ) | ||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.