Find Greatest Common Divisor of 196 and 250, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 250 $ by $ 196 $ and get the remainder
The remainder is positive ($ 54 > 0 $), so we will continue with division.
Step 2 :
Divide $ 196 $ by $ \color{blue}{ 54 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 3 :
Divide $ 54 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 4 :
Divide $ 34 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 5 :
Divide $ 20 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 6 :
Divide $ 14 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 6 $ 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.
| 250 | : | 196 | = | 1 | remainder ( 54 ) | ||||||||||||
| 196 | : | 54 | = | 3 | remainder ( 34 ) | ||||||||||||
| 54 | : | 34 | = | 1 | remainder ( 20 ) | ||||||||||||
| 34 | : | 20 | = | 1 | remainder ( 14 ) | ||||||||||||
| 20 | : | 14 | = | 1 | remainder ( 6 ) | ||||||||||||
| 14 | : | 6 | = | 2 | remainder ( 2 ) | ||||||||||||
| 6 | : | 2 | = | 3 | remainder ( 0 ) | ||||||||||||
| GCD = 2 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.