The GCD of given numbers is 9.
Step 1 :
Divide $ 243 $ by $ 198 $ and get the remainder
The remainder is positive ($ 45 > 0 $), so we will continue with division.
Step 2 :
Divide $ 198 $ by $ \color{blue}{ 45 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 3 :
Divide $ 45 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 4 :
Divide $ 18 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 9 }} $.
We can summarize an algorithm into a following table.
243 | : | 198 | = | 1 | remainder ( 45 ) | ||||||
198 | : | 45 | = | 4 | remainder ( 18 ) | ||||||
45 | : | 18 | = | 2 | remainder ( 9 ) | ||||||
18 | : | 9 | = | 2 | remainder ( 0 ) | ||||||
GCD = 9 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.