The GCD of given numbers is 1.
Step 1 :
Divide $ 765844 $ by $ 8365 $ and get the remainder
The remainder is positive ($ 4629 > 0 $), so we will continue with division.
Step 2 :
Divide $ 8365 $ by $ \color{blue}{ 4629 } $ and get the remainder
The remainder is still positive ($ 3736 > 0 $), so we will continue with division.
Step 3 :
Divide $ 4629 $ by $ \color{blue}{ 3736 } $ and get the remainder
The remainder is still positive ($ 893 > 0 $), so we will continue with division.
Step 4 :
Divide $ 3736 $ by $ \color{blue}{ 893 } $ and get the remainder
The remainder is still positive ($ 164 > 0 $), so we will continue with division.
Step 5 :
Divide $ 893 $ by $ \color{blue}{ 164 } $ and get the remainder
The remainder is still positive ($ 73 > 0 $), so we will continue with division.
Step 6 :
Divide $ 164 $ by $ \color{blue}{ 73 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 7 :
Divide $ 73 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
Divide $ 18 $ 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.
765844 | : | 8365 | = | 91 | remainder ( 4629 ) | ||||||||||||||
8365 | : | 4629 | = | 1 | remainder ( 3736 ) | ||||||||||||||
4629 | : | 3736 | = | 1 | remainder ( 893 ) | ||||||||||||||
3736 | : | 893 | = | 4 | remainder ( 164 ) | ||||||||||||||
893 | : | 164 | = | 5 | remainder ( 73 ) | ||||||||||||||
164 | : | 73 | = | 2 | remainder ( 18 ) | ||||||||||||||
73 | : | 18 | = | 4 | remainder ( 1 ) | ||||||||||||||
18 | : | 1 | = | 18 | remainder ( 0 ) | ||||||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.