Find Greatest Common Divisor of 195 and 340, using Euclidean algorithm.
Answer
The GCD of given numbers is 5.
Explanation
Step 1 :
Divide $ 340 $ by $ 195 $ and get the remainder
The remainder is positive ($ 145 > 0 $), so we will continue with division.
Step 2 :
Divide $ 195 $ by $ \color{blue}{ 145 } $ and get the remainder
The remainder is still positive ($ 50 > 0 $), so we will continue with division.
Step 3 :
Divide $ 145 $ by $ \color{blue}{ 50 } $ and get the remainder
The remainder is still positive ($ 45 > 0 $), so we will continue with division.
Step 4 :
Divide $ 50 $ by $ \color{blue}{ 45 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 5 :
Divide $ 45 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 5 }} $.
We can summarize an algorithm into a following table.
| 340 | : | 195 | = | 1 | remainder ( 145 ) | ||||||||
| 195 | : | 145 | = | 1 | remainder ( 50 ) | ||||||||
| 145 | : | 50 | = | 2 | remainder ( 45 ) | ||||||||
| 50 | : | 45 | = | 1 | remainder ( 5 ) | ||||||||
| 45 | : | 5 | = | 9 | remainder ( 0 ) | ||||||||
| GCD = 5 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.