The GCD of given numbers is 1.
Step 1 :
Divide $ 68 $ by $ 41 $ and get the remainder
The remainder is positive ($ 27 > 0 $), so we will continue with division.
Step 2 :
Divide $ 41 $ by $ \color{blue}{ 27 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 3 :
Divide $ 27 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 4 :
Divide $ 14 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 13 $ 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.
68 | : | 41 | = | 1 | remainder ( 27 ) | ||||||||
41 | : | 27 | = | 1 | remainder ( 14 ) | ||||||||
27 | : | 14 | = | 1 | remainder ( 13 ) | ||||||||
14 | : | 13 | = | 1 | remainder ( 1 ) | ||||||||
13 | : | 1 | = | 13 | remainder ( 0 ) | ||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.