Step 1 :
Divide $ 8201782117 $ by $ 130963810 $ and get the remainder

$$ 8201782117 : 130963810 = 62 \text{ ( remainder is } \color{blue}{ 82025897 } \text{ ) } $$

The remainder is positive ($ 82025897 > 0 $), so we will continue with division.

Step 2 :
Divide $ 130963810 $ by $ \color{blue}{ 82025897 } $ and get the remainder

$$ 130963810 : 82025897 = 1 \text{ ( remainder is } \color{blue}{ 48937913 } \text{ ) } $$

The remainder is still positive ($ 48937913 > 0 $), so we will continue with division.

Step 3 :
Divide $ 82025897 $ by $ \color{blue}{ 48937913 } $ and get the remainder

$$ 82025897 : 48937913 = 1 \text{ ( remainder is } \color{blue}{ 33087984 } \text{ ) } $$

The remainder is still positive ($ 33087984 > 0 $), so we will continue with division.

Step 4 :
Divide $ 48937913 $ by $ \color{blue}{ 33087984 } $ and get the remainder

$$ 48937913 : 33087984 = 1 \text{ ( remainder is } \color{blue}{ 15849929 } \text{ ) } $$

The remainder is still positive ($ 15849929 > 0 $), so we will continue with division.

Step 5 :
Divide $ 33087984 $ by $ \color{blue}{ 15849929 } $ and get the remainder

$$ 33087984 : 15849929 = 2 \text{ ( remainder is } \color{blue}{ 1388126 } \text{ ) } $$

The remainder is still positive ($ 1388126 > 0 $), so we will continue with division.

Step 6 :
Divide $ 15849929 $ by $ \color{blue}{ 1388126 } $ and get the remainder

$$ 15849929 : 1388126 = 11 \text{ ( remainder is } \color{blue}{ 580543 } \text{ ) } $$

The remainder is still positive ($ 580543 > 0 $), so we will continue with division.

Step 7 :
Divide $ 1388126 $ by $ \color{blue}{ 580543 } $ and get the remainder

$$ 1388126 : 580543 = 2 \text{ ( remainder is } \color{blue}{ 227040 } \text{ ) } $$

The remainder is still positive ($ 227040 > 0 $), so we will continue with division.

Step 8 :
Divide $ 580543 $ by $ \color{blue}{ 227040 } $ and get the remainder

$$ 580543 : 227040 = 2 \text{ ( remainder is } \color{blue}{ 126463 } \text{ ) } $$

The remainder is still positive ($ 126463 > 0 $), so we will continue with division.

Step 9 :
Divide $ 227040 $ by $ \color{blue}{ 126463 } $ and get the remainder

$$ 227040 : 126463 = 1 \text{ ( remainder is } \color{blue}{ 100577 } \text{ ) } $$

The remainder is still positive ($ 100577 > 0 $), so we will continue with division.

Step 10 :
Divide $ 126463 $ by $ \color{blue}{ 100577 } $ and get the remainder

$$ 126463 : 100577 = 1 \text{ ( remainder is } \color{blue}{ 25886 } \text{ ) } $$

The remainder is still positive ($ 25886 > 0 $), so we will continue with division.

Step 11 :
Divide $ 100577 $ by $ \color{blue}{ 25886 } $ and get the remainder

$$ 100577 : 25886 = 3 \text{ ( remainder is } \color{blue}{ 22919 } \text{ ) } $$

The remainder is still positive ($ 22919 > 0 $), so we will continue with division.

Step 12 :
Divide $ 25886 $ by $ \color{blue}{ 22919 } $ and get the remainder

$$ 25886 : 22919 = 1 \text{ ( remainder is } \color{blue}{ 2967 } \text{ ) } $$

The remainder is still positive ($ 2967 > 0 $), so we will continue with division.

Step 13 :
Divide $ 22919 $ by $ \color{blue}{ 2967 } $ and get the remainder

$$ 22919 : 2967 = 7 \text{ ( remainder is } \color{blue}{ 2150 } \text{ ) } $$

The remainder is still positive ($ 2150 > 0 $), so we will continue with division.

Step 14 :
Divide $ 2967 $ by $ \color{blue}{ 2150 } $ and get the remainder

$$ 2967 : 2150 = 1 \text{ ( remainder is } \color{blue}{ 817 } \text{ ) } $$

The remainder is still positive ($ 817 > 0 $), so we will continue with division.

Step 15 :
Divide $ 2150 $ by $ \color{blue}{ 817 } $ and get the remainder

$$ 2150 : 817 = 2 \text{ ( remainder is } \color{blue}{ 516 } \text{ ) } $$

The remainder is still positive ($ 516 > 0 $), so we will continue with division.

Step 16 :
Divide $ 817 $ by $ \color{blue}{ 516 } $ and get the remainder

$$ 817 : 516 = 1 \text{ ( remainder is } \color{blue}{ 301 } \text{ ) } $$

The remainder is still positive ($ 301 > 0 $), so we will continue with division.

Step 17 :
Divide $ 516 $ by $ \color{blue}{ 301 } $ and get the remainder

$$ 516 : 301 = 1 \text{ ( remainder is } \color{blue}{ 215 } \text{ ) } $$

The remainder is still positive ($ 215 > 0 $), so we will continue with division.

Step 18 :
Divide $ 301 $ by $ \color{blue}{ 215 } $ and get the remainder

$$ 301 : 215 = 1 \text{ ( remainder is } \color{blue}{ 86 } \text{ ) } $$

The remainder is still positive ($ 86 > 0 $), so we will continue with division.

Step 19 :
Divide $ 215 $ by $ \color{blue}{ 86 } $ and get the remainder

$$ 215 : 86 = 2 \text{ ( remainder is } \color{blue}{ 43 } \text{ ) } $$

The remainder is still positive ($ 43 > 0 $), so we will continue with division.

Step 20 :
Divide $ 86 $ by $ \color{blue}{ 43 } $ and get the remainder

$$ 86 : \color{blue}{ \boxed { 43 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 43 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

GCD Calculator