Find Greatest Common Divisor of 807 and 481, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 807 $ by $ 481 $ and get the remainder
The remainder is positive ($ 326 > 0 $), so we will continue with division.
Step 2 :
Divide $ 481 $ by $ \color{blue}{ 326 } $ and get the remainder
The remainder is still positive ($ 155 > 0 $), so we will continue with division.
Step 3 :
Divide $ 326 $ by $ \color{blue}{ 155 } $ and get the remainder
The remainder is still positive ($ 16 > 0 $), so we will continue with division.
Step 4 :
Divide $ 155 $ by $ \color{blue}{ 16 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 5 :
Divide $ 16 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 6 :
Divide $ 11 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 5 $ 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.
| 807 | : | 481 | = | 1 | remainder ( 326 ) | ||||||||||||
| 481 | : | 326 | = | 1 | remainder ( 155 ) | ||||||||||||
| 326 | : | 155 | = | 2 | remainder ( 16 ) | ||||||||||||
| 155 | : | 16 | = | 9 | remainder ( 11 ) | ||||||||||||
| 16 | : | 11 | = | 1 | remainder ( 5 ) | ||||||||||||
| 11 | : | 5 | = | 2 | remainder ( 1 ) | ||||||||||||
| 5 | : | 1 | = | 5 | remainder ( 0 ) | ||||||||||||
| GCD = 1 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.