Find Greatest Common Divisor of 765844 and 8362, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 765844 $ by $ 8362 $ and get the remainder
The remainder is positive ($ 4902 > 0 $), so we will continue with division.
Step 2 :
Divide $ 8362 $ by $ \color{blue}{ 4902 } $ and get the remainder
The remainder is still positive ($ 3460 > 0 $), so we will continue with division.
Step 3 :
Divide $ 4902 $ by $ \color{blue}{ 3460 } $ and get the remainder
The remainder is still positive ($ 1442 > 0 $), so we will continue with division.
Step 4 :
Divide $ 3460 $ by $ \color{blue}{ 1442 } $ and get the remainder
The remainder is still positive ($ 576 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1442 $ by $ \color{blue}{ 576 } $ and get the remainder
The remainder is still positive ($ 290 > 0 $), so we will continue with division.
Step 6 :
Divide $ 576 $ by $ \color{blue}{ 290 } $ and get the remainder
The remainder is still positive ($ 286 > 0 $), so we will continue with division.
Step 7 :
Divide $ 290 $ by $ \color{blue}{ 286 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 8 :
Divide $ 286 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 9 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
| 765844 | : | 8362 | = | 91 | remainder ( 4902 ) | ||||||||||||||||
| 8362 | : | 4902 | = | 1 | remainder ( 3460 ) | ||||||||||||||||
| 4902 | : | 3460 | = | 1 | remainder ( 1442 ) | ||||||||||||||||
| 3460 | : | 1442 | = | 2 | remainder ( 576 ) | ||||||||||||||||
| 1442 | : | 576 | = | 2 | remainder ( 290 ) | ||||||||||||||||
| 576 | : | 290 | = | 1 | remainder ( 286 ) | ||||||||||||||||
| 290 | : | 286 | = | 1 | remainder ( 4 ) | ||||||||||||||||
| 286 | : | 4 | = | 71 | remainder ( 2 ) | ||||||||||||||||
| 4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||||||||||||
| GCD = 2 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.