The GCD of given numbers is 1.
Step 1 :
Divide $ 76587 $ by $ 836 $ and get the remainder
The remainder is positive ($ 511 > 0 $), so we will continue with division.
Step 2 :
Divide $ 836 $ by $ \color{blue}{ 511 } $ and get the remainder
The remainder is still positive ($ 325 > 0 $), so we will continue with division.
Step 3 :
Divide $ 511 $ by $ \color{blue}{ 325 } $ and get the remainder
The remainder is still positive ($ 186 > 0 $), so we will continue with division.
Step 4 :
Divide $ 325 $ by $ \color{blue}{ 186 } $ and get the remainder
The remainder is still positive ($ 139 > 0 $), so we will continue with division.
Step 5 :
Divide $ 186 $ by $ \color{blue}{ 139 } $ and get the remainder
The remainder is still positive ($ 47 > 0 $), so we will continue with division.
Step 6 :
Divide $ 139 $ by $ \color{blue}{ 47 } $ and get the remainder
The remainder is still positive ($ 45 > 0 $), so we will continue with division.
Step 7 :
Divide $ 47 $ by $ \color{blue}{ 45 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 8 :
Divide $ 45 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 9 :
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.
76587 | : | 836 | = | 91 | remainder ( 511 ) | ||||||||||||||||
836 | : | 511 | = | 1 | remainder ( 325 ) | ||||||||||||||||
511 | : | 325 | = | 1 | remainder ( 186 ) | ||||||||||||||||
325 | : | 186 | = | 1 | remainder ( 139 ) | ||||||||||||||||
186 | : | 139 | = | 1 | remainder ( 47 ) | ||||||||||||||||
139 | : | 47 | = | 2 | remainder ( 45 ) | ||||||||||||||||
47 | : | 45 | = | 1 | remainder ( 2 ) | ||||||||||||||||
45 | : | 2 | = | 22 | 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.