The GCD of given numbers is 1.
Step 1 :
Divide $ 3543 $ by $ 1547 $ and get the remainder
The remainder is positive ($ 449 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1547 $ by $ \color{blue}{ 449 } $ and get the remainder
The remainder is still positive ($ 200 > 0 $), so we will continue with division.
Step 3 :
Divide $ 449 $ by $ \color{blue}{ 200 } $ and get the remainder
The remainder is still positive ($ 49 > 0 $), so we will continue with division.
Step 4 :
Divide $ 200 $ by $ \color{blue}{ 49 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 5 :
Divide $ 49 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 4 $ 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.
3543 | : | 1547 | = | 2 | remainder ( 449 ) | ||||||||||
1547 | : | 449 | = | 3 | remainder ( 200 ) | ||||||||||
449 | : | 200 | = | 2 | remainder ( 49 ) | ||||||||||
200 | : | 49 | = | 4 | remainder ( 4 ) | ||||||||||
49 | : | 4 | = | 12 | remainder ( 1 ) | ||||||||||
4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.