Find Greatest Common Divisor of 196 and 340, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 340 $ by $ 196 $ and get the remainder
The remainder is positive ($ 144 > 0 $), so we will continue with division.
Step 2 :
Divide $ 196 $ by $ \color{blue}{ 144 } $ and get the remainder
The remainder is still positive ($ 52 > 0 $), so we will continue with division.
Step 3 :
Divide $ 144 $ by $ \color{blue}{ 52 } $ and get the remainder
The remainder is still positive ($ 40 > 0 $), so we will continue with division.
Step 4 :
Divide $ 52 $ by $ \color{blue}{ 40 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 5 :
Divide $ 40 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 12 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 340 | : | 196 | = | 1 | remainder ( 144 ) | ||||||||||
| 196 | : | 144 | = | 1 | remainder ( 52 ) | ||||||||||
| 144 | : | 52 | = | 2 | remainder ( 40 ) | ||||||||||
| 52 | : | 40 | = | 1 | remainder ( 12 ) | ||||||||||
| 40 | : | 12 | = | 3 | remainder ( 4 ) | ||||||||||
| 12 | : | 4 | = | 3 | remainder ( 0 ) | ||||||||||
| GCD = 4 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.