Step 1 :
Divide $ 9353919043 $ by $ 12091 $ and get the remainder

$$ 9353919043 : 12091 = 773626 \text{ ( remainder is } \color{blue}{ 7077 } \text{ ) } $$

The remainder is positive ($ 7077 > 0 $), so we will continue with division.

Step 2 :
Divide $ 12091 $ by $ \color{blue}{ 7077 } $ and get the remainder

$$ 12091 : 7077 = 1 \text{ ( remainder is } \color{blue}{ 5014 } \text{ ) } $$

The remainder is still positive ($ 5014 > 0 $), so we will continue with division.

Step 3 :
Divide $ 7077 $ by $ \color{blue}{ 5014 } $ and get the remainder

$$ 7077 : 5014 = 1 \text{ ( remainder is } \color{blue}{ 2063 } \text{ ) } $$

The remainder is still positive ($ 2063 > 0 $), so we will continue with division.

Step 4 :
Divide $ 5014 $ by $ \color{blue}{ 2063 } $ and get the remainder

$$ 5014 : 2063 = 2 \text{ ( remainder is } \color{blue}{ 888 } \text{ ) } $$

The remainder is still positive ($ 888 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2063 $ by $ \color{blue}{ 888 } $ and get the remainder

$$ 2063 : 888 = 2 \text{ ( remainder is } \color{blue}{ 287 } \text{ ) } $$

The remainder is still positive ($ 287 > 0 $), so we will continue with division.

Step 6 :
Divide $ 888 $ by $ \color{blue}{ 287 } $ and get the remainder

$$ 888 : 287 = 3 \text{ ( remainder is } \color{blue}{ 27 } \text{ ) } $$

The remainder is still positive ($ 27 > 0 $), so we will continue with division.

Step 7 :
Divide $ 287 $ by $ \color{blue}{ 27 } $ and get the remainder

$$ 287 : 27 = 10 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 8 :
Divide $ 27 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 27 : 17 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 9 :
Divide $ 17 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 17 : 10 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 10 :
Divide $ 10 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 10 : 7 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 11 :
Divide $ 7 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 7 : 3 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 12 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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