The GCD of given numbers is 1.
Step 1 :
Divide $ 547 $ by $ 189 $ and get the remainder
The remainder is positive ($ 169 > 0 $), so we will continue with division.
Step 2 :
Divide $ 189 $ by $ \color{blue}{ 169 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 3 :
Divide $ 169 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 4 :
Divide $ 20 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 9 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 2 $ 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.
547 | : | 189 | = | 2 | remainder ( 169 ) | ||||||||||
189 | : | 169 | = | 1 | remainder ( 20 ) | ||||||||||
169 | : | 20 | = | 8 | remainder ( 9 ) | ||||||||||
20 | : | 9 | = | 2 | remainder ( 2 ) | ||||||||||
9 | : | 2 | = | 4 | remainder ( 1 ) | ||||||||||
2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.