Find Greatest Common Divisor of 8071 and 4655, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 :
Divide $ 8071 $ by $ 4655 $ and get the remainder
The remainder is positive ($ 3416 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4655 $ by $ \color{blue}{ 3416 } $ and get the remainder
The remainder is still positive ($ 1239 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3416 $ by $ \color{blue}{ 1239 } $ and get the remainder
The remainder is still positive ($ 938 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1239 $ by $ \color{blue}{ 938 } $ and get the remainder
The remainder is still positive ($ 301 > 0 $), so we will continue with division.
Step 5 :
Divide $ 938 $ by $ \color{blue}{ 301 } $ and get the remainder
The remainder is still positive ($ 35 > 0 $), so we will continue with division.
Step 6 :
Divide $ 301 $ by $ \color{blue}{ 35 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 7 :
Divide $ 35 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 8 :
Divide $ 21 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 9 :
Divide $ 14 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
| 8071 | : | 4655 | = | 1 | remainder ( 3416 ) | ||||||||||||||||
| 4655 | : | 3416 | = | 1 | remainder ( 1239 ) | ||||||||||||||||
| 3416 | : | 1239 | = | 2 | remainder ( 938 ) | ||||||||||||||||
| 1239 | : | 938 | = | 1 | remainder ( 301 ) | ||||||||||||||||
| 938 | : | 301 | = | 3 | remainder ( 35 ) | ||||||||||||||||
| 301 | : | 35 | = | 8 | remainder ( 21 ) | ||||||||||||||||
| 35 | : | 21 | = | 1 | remainder ( 14 ) | ||||||||||||||||
| 21 | : | 14 | = | 1 | remainder ( 7 ) | ||||||||||||||||
| 14 | : | 7 | = | 2 | remainder ( 0 ) | ||||||||||||||||
| GCD = 7 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.