The GCD of given numbers is 2.
Step 1 :
Divide $ 230 $ by $ 136 $ and get the remainder
The remainder is positive ($ 94 > 0 $), so we will continue with division.
Step 2 :
Divide $ 136 $ by $ \color{blue}{ 94 } $ and get the remainder
The remainder is still positive ($ 42 > 0 $), so we will continue with division.
Step 3 :
Divide $ 94 $ by $ \color{blue}{ 42 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 42 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 10 $ 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.
230 | : | 136 | = | 1 | remainder ( 94 ) | ||||||||
136 | : | 94 | = | 1 | remainder ( 42 ) | ||||||||
94 | : | 42 | = | 2 | remainder ( 10 ) | ||||||||
42 | : | 10 | = | 4 | remainder ( 2 ) | ||||||||
10 | : | 2 | = | 5 | remainder ( 0 ) | ||||||||
GCD = 2 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.