The GCD of given numbers is 28.
Step 1 :
Divide $ 504 $ by $ 308 $ and get the remainder
The remainder is positive ($ 196 > 0 $), so we will continue with division.
Step 2 :
Divide $ 308 $ by $ \color{blue}{ 196 } $ and get the remainder
The remainder is still positive ($ 112 > 0 $), so we will continue with division.
Step 3 :
Divide $ 196 $ by $ \color{blue}{ 112 } $ and get the remainder
The remainder is still positive ($ 84 > 0 $), so we will continue with division.
Step 4 :
Divide $ 112 $ by $ \color{blue}{ 84 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 5 :
Divide $ 84 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 28 }} $.
We can summarize an algorithm into a following table.
504 | : | 308 | = | 1 | remainder ( 196 ) | ||||||||
308 | : | 196 | = | 1 | remainder ( 112 ) | ||||||||
196 | : | 112 | = | 1 | remainder ( 84 ) | ||||||||
112 | : | 84 | = | 1 | remainder ( 28 ) | ||||||||
84 | : | 28 | = | 3 | remainder ( 0 ) | ||||||||
GCD = 28 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.