The GCD of given numbers is 1.
Step 1 :
Divide $ 71 $ by $ 41 $ and get the remainder
The remainder is positive ($ 30 > 0 $), so we will continue with division.
Step 2 :
Divide $ 41 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 3 :
Divide $ 30 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 4 :
Divide $ 11 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 8 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
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.
71 | : | 41 | = | 1 | remainder ( 30 ) | ||||||||||||
41 | : | 30 | = | 1 | remainder ( 11 ) | ||||||||||||
30 | : | 11 | = | 2 | remainder ( 8 ) | ||||||||||||
11 | : | 8 | = | 1 | remainder ( 3 ) | ||||||||||||
8 | : | 3 | = | 2 | remainder ( 2 ) | ||||||||||||
3 | : | 2 | = | 1 | 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.