The GCD of given numbers is 14.
Step 1 :
Divide $ 868 $ by $ 378 $ and get the remainder
The remainder is positive ($ 112 > 0 $), so we will continue with division.
Step 2 :
Divide $ 378 $ by $ \color{blue}{ 112 } $ and get the remainder
The remainder is still positive ($ 42 > 0 $), so we will continue with division.
Step 3 :
Divide $ 112 $ by $ \color{blue}{ 42 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 4 :
Divide $ 42 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 5 :
Divide $ 28 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 14 }} $.
We can summarize an algorithm into a following table.
868 | : | 378 | = | 2 | remainder ( 112 ) | ||||||||
378 | : | 112 | = | 3 | remainder ( 42 ) | ||||||||
112 | : | 42 | = | 2 | remainder ( 28 ) | ||||||||
42 | : | 28 | = | 1 | remainder ( 14 ) | ||||||||
28 | : | 14 | = | 2 | remainder ( 0 ) | ||||||||
GCD = 14 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.