Find Greatest Common Divisor of 343 and 237, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 343 $ by $ 237 $ and get the remainder
The remainder is positive ($ 106 > 0 $), so we will continue with division.
Step 2 :
Divide $ 237 $ by $ \color{blue}{ 106 } $ and get the remainder
The remainder is still positive ($ 25 > 0 $), so we will continue with division.
Step 3 :
Divide $ 106 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 25 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 6 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 343 | : | 237 | = | 1 | remainder ( 106 ) | ||||||||
| 237 | : | 106 | = | 2 | remainder ( 25 ) | ||||||||
| 106 | : | 25 | = | 4 | remainder ( 6 ) | ||||||||
| 25 | : | 6 | = | 4 | remainder ( 1 ) | ||||||||
| 6 | : | 1 | = | 6 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.