Find Greatest Common Divisor of 765845 and 836, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 765845 $ by $ 836 $ and get the remainder
The remainder is positive ($ 69 > 0 $), so we will continue with division.
Step 2 :
Divide $ 836 $ by $ \color{blue}{ 69 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 3 :
Divide $ 69 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 4 :
Divide $ 8 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 5 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 2 $ 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.
| 765845 | : | 836 | = | 916 | remainder ( 69 ) | ||||||||||||
| 836 | : | 69 | = | 12 | remainder ( 8 ) | ||||||||||||
| 69 | : | 8 | = | 8 | remainder ( 5 ) | ||||||||||||
| 8 | : | 5 | = | 1 | remainder ( 3 ) | ||||||||||||
| 5 | : | 3 | = | 1 | remainder ( 2 ) | ||||||||||||
| 3 | : | 2 | = | 1 | remainder ( 1 ) | ||||||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||
| GCD = 1 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.