Find Greatest Common Divisor of 6437 and 2393, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 6437 $ by $ 2393 $ and get the remainder
The remainder is positive ($ 1651 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2393 $ by $ \color{blue}{ 1651 } $ and get the remainder
The remainder is still positive ($ 742 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1651 $ by $ \color{blue}{ 742 } $ and get the remainder
The remainder is still positive ($ 167 > 0 $), so we will continue with division.
Step 4 :
Divide $ 742 $ by $ \color{blue}{ 167 } $ and get the remainder
The remainder is still positive ($ 74 > 0 $), so we will continue with division.
Step 5 :
Divide $ 167 $ by $ \color{blue}{ 74 } $ and get the remainder
The remainder is still positive ($ 19 > 0 $), so we will continue with division.
Step 6 :
Divide $ 74 $ by $ \color{blue}{ 19 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 7 :
Divide $ 19 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 8 :
Divide $ 17 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 9 :
Divide $ 2 $ 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.
| 6437 | : | 2393 | = | 2 | remainder ( 1651 ) | ||||||||||||||||
| 2393 | : | 1651 | = | 1 | remainder ( 742 ) | ||||||||||||||||
| 1651 | : | 742 | = | 2 | remainder ( 167 ) | ||||||||||||||||
| 742 | : | 167 | = | 4 | remainder ( 74 ) | ||||||||||||||||
| 167 | : | 74 | = | 2 | remainder ( 19 ) | ||||||||||||||||
| 74 | : | 19 | = | 3 | remainder ( 17 ) | ||||||||||||||||
| 19 | : | 17 | = | 1 | remainder ( 2 ) | ||||||||||||||||
| 17 | : | 2 | = | 8 | remainder ( 1 ) | ||||||||||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||||||
| GCD = 1 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.