Find Greatest Common Divisor of 6638 and 22783, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 22783 $ by $ 6638 $ and get the remainder
The remainder is positive ($ 2869 > 0 $), so we will continue with division.
Step 2 :
Divide $ 6638 $ by $ \color{blue}{ 2869 } $ and get the remainder
The remainder is still positive ($ 900 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2869 $ by $ \color{blue}{ 900 } $ and get the remainder
The remainder is still positive ($ 169 > 0 $), so we will continue with division.
Step 4 :
Divide $ 900 $ by $ \color{blue}{ 169 } $ and get the remainder
The remainder is still positive ($ 55 > 0 $), so we will continue with division.
Step 5 :
Divide $ 169 $ by $ \color{blue}{ 55 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 6 :
Divide $ 55 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 7 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 3 $ 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.
| 22783 | : | 6638 | = | 3 | remainder ( 2869 ) | ||||||||||||||
| 6638 | : | 2869 | = | 2 | remainder ( 900 ) | ||||||||||||||
| 2869 | : | 900 | = | 3 | remainder ( 169 ) | ||||||||||||||
| 900 | : | 169 | = | 5 | remainder ( 55 ) | ||||||||||||||
| 169 | : | 55 | = | 3 | remainder ( 4 ) | ||||||||||||||
| 55 | : | 4 | = | 13 | remainder ( 3 ) | ||||||||||||||
| 4 | : | 3 | = | 1 | remainder ( 1 ) | ||||||||||||||
| 3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||||||||
| GCD = 1 | |||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.