The GCD of given numbers is 2.
Step 1 :
Divide $ 398 $ by $ 294 $ and get the remainder
The remainder is positive ($ 104 > 0 $), so we will continue with division.
Step 2 :
Divide $ 294 $ by $ \color{blue}{ 104 } $ and get the remainder
The remainder is still positive ($ 86 > 0 $), so we will continue with division.
Step 3 :
Divide $ 104 $ by $ \color{blue}{ 86 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 4 :
Divide $ 86 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 5 :
Divide $ 18 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 14 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
398 | : | 294 | = | 1 | remainder ( 104 ) | ||||||||||||
294 | : | 104 | = | 2 | remainder ( 86 ) | ||||||||||||
104 | : | 86 | = | 1 | remainder ( 18 ) | ||||||||||||
86 | : | 18 | = | 4 | remainder ( 14 ) | ||||||||||||
18 | : | 14 | = | 1 | remainder ( 4 ) | ||||||||||||
14 | : | 4 | = | 3 | remainder ( 2 ) | ||||||||||||
4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.