The GCD of given numbers is 263.
Step 1 :
Divide $ 117035 $ by $ 91261 $ and get the remainder
The remainder is positive ($ 25774 > 0 $), so we will continue with division.
Step 2 :
Divide $ 91261 $ by $ \color{blue}{ 25774 } $ and get the remainder
The remainder is still positive ($ 13939 > 0 $), so we will continue with division.
Step 3 :
Divide $ 25774 $ by $ \color{blue}{ 13939 } $ and get the remainder
The remainder is still positive ($ 11835 > 0 $), so we will continue with division.
Step 4 :
Divide $ 13939 $ by $ \color{blue}{ 11835 } $ and get the remainder
The remainder is still positive ($ 2104 > 0 $), so we will continue with division.
Step 5 :
Divide $ 11835 $ by $ \color{blue}{ 2104 } $ and get the remainder
The remainder is still positive ($ 1315 > 0 $), so we will continue with division.
Step 6 :
Divide $ 2104 $ by $ \color{blue}{ 1315 } $ and get the remainder
The remainder is still positive ($ 789 > 0 $), so we will continue with division.
Step 7 :
Divide $ 1315 $ by $ \color{blue}{ 789 } $ and get the remainder
The remainder is still positive ($ 526 > 0 $), so we will continue with division.
Step 8 :
Divide $ 789 $ by $ \color{blue}{ 526 } $ and get the remainder
The remainder is still positive ($ 263 > 0 $), so we will continue with division.
Step 9 :
Divide $ 526 $ by $ \color{blue}{ 263 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 263 }} $.
We can summarize an algorithm into a following table.
117035 | : | 91261 | = | 1 | remainder ( 25774 ) | ||||||||||||||||
91261 | : | 25774 | = | 3 | remainder ( 13939 ) | ||||||||||||||||
25774 | : | 13939 | = | 1 | remainder ( 11835 ) | ||||||||||||||||
13939 | : | 11835 | = | 1 | remainder ( 2104 ) | ||||||||||||||||
11835 | : | 2104 | = | 5 | remainder ( 1315 ) | ||||||||||||||||
2104 | : | 1315 | = | 1 | remainder ( 789 ) | ||||||||||||||||
1315 | : | 789 | = | 1 | remainder ( 526 ) | ||||||||||||||||
789 | : | 526 | = | 1 | remainder ( 263 ) | ||||||||||||||||
526 | : | 263 | = | 2 | remainder ( 0 ) | ||||||||||||||||
GCD = 263 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.