Find Greatest Common Divisor of 4284 and 8219, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 8219 $ by $ 4284 $ and get the remainder
The remainder is positive ($ 3935 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4284 $ by $ \color{blue}{ 3935 } $ and get the remainder
The remainder is still positive ($ 349 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3935 $ by $ \color{blue}{ 349 } $ and get the remainder
The remainder is still positive ($ 96 > 0 $), so we will continue with division.
Step 4 :
Divide $ 349 $ by $ \color{blue}{ 96 } $ and get the remainder
The remainder is still positive ($ 61 > 0 $), so we will continue with division.
Step 5 :
Divide $ 96 $ by $ \color{blue}{ 61 } $ and get the remainder
The remainder is still positive ($ 35 > 0 $), so we will continue with division.
Step 6 :
Divide $ 61 $ by $ \color{blue}{ 35 } $ and get the remainder
The remainder is still positive ($ 26 > 0 $), so we will continue with division.
Step 7 :
Divide $ 35 $ by $ \color{blue}{ 26 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 8 :
Divide $ 26 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 9 :
Divide $ 9 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 10 :
Divide $ 8 $ 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.
| 8219 | : | 4284 | = | 1 | remainder ( 3935 ) | ||||||||||||||||||
| 4284 | : | 3935 | = | 1 | remainder ( 349 ) | ||||||||||||||||||
| 3935 | : | 349 | = | 11 | remainder ( 96 ) | ||||||||||||||||||
| 349 | : | 96 | = | 3 | remainder ( 61 ) | ||||||||||||||||||
| 96 | : | 61 | = | 1 | remainder ( 35 ) | ||||||||||||||||||
| 61 | : | 35 | = | 1 | remainder ( 26 ) | ||||||||||||||||||
| 35 | : | 26 | = | 1 | remainder ( 9 ) | ||||||||||||||||||
| 26 | : | 9 | = | 2 | remainder ( 8 ) | ||||||||||||||||||
| 9 | : | 8 | = | 1 | remainder ( 1 ) | ||||||||||||||||||
| 8 | : | 1 | = | 8 | remainder ( 0 ) | ||||||||||||||||||
| GCD = 1 | |||||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.