Step 1 :
Divide $ 1021763679 $ by $ 519424709 $ and get the remainder

$$ 1021763679 : 519424709 = 1 \text{ ( remainder is } \color{blue}{ 502338970 } \text{ ) } $$

The remainder is positive ($ 502338970 > 0 $), so we will continue with division.

Step 2 :
Divide $ 519424709 $ by $ \color{blue}{ 502338970 } $ and get the remainder

$$ 519424709 : 502338970 = 1 \text{ ( remainder is } \color{blue}{ 17085739 } \text{ ) } $$

The remainder is still positive ($ 17085739 > 0 $), so we will continue with division.

Step 3 :
Divide $ 502338970 $ by $ \color{blue}{ 17085739 } $ and get the remainder

$$ 502338970 : 17085739 = 29 \text{ ( remainder is } \color{blue}{ 6852539 } \text{ ) } $$

The remainder is still positive ($ 6852539 > 0 $), so we will continue with division.

Step 4 :
Divide $ 17085739 $ by $ \color{blue}{ 6852539 } $ and get the remainder

$$ 17085739 : 6852539 = 2 \text{ ( remainder is } \color{blue}{ 3380661 } \text{ ) } $$

The remainder is still positive ($ 3380661 > 0 $), so we will continue with division.

Step 5 :
Divide $ 6852539 $ by $ \color{blue}{ 3380661 } $ and get the remainder

$$ 6852539 : 3380661 = 2 \text{ ( remainder is } \color{blue}{ 91217 } \text{ ) } $$

The remainder is still positive ($ 91217 > 0 $), so we will continue with division.

Step 6 :
Divide $ 3380661 $ by $ \color{blue}{ 91217 } $ and get the remainder

$$ 3380661 : 91217 = 37 \text{ ( remainder is } \color{blue}{ 5632 } \text{ ) } $$

The remainder is still positive ($ 5632 > 0 $), so we will continue with division.

Step 7 :
Divide $ 91217 $ by $ \color{blue}{ 5632 } $ and get the remainder

$$ 91217 : 5632 = 16 \text{ ( remainder is } \color{blue}{ 1105 } \text{ ) } $$

The remainder is still positive ($ 1105 > 0 $), so we will continue with division.

Step 8 :
Divide $ 5632 $ by $ \color{blue}{ 1105 } $ and get the remainder

$$ 5632 : 1105 = 5 \text{ ( remainder is } \color{blue}{ 107 } \text{ ) } $$

The remainder is still positive ($ 107 > 0 $), so we will continue with division.

Step 9 :
Divide $ 1105 $ by $ \color{blue}{ 107 } $ and get the remainder

$$ 1105 : 107 = 10 \text{ ( remainder is } \color{blue}{ 35 } \text{ ) } $$

The remainder is still positive ($ 35 > 0 $), so we will continue with division.

Step 10 :
Divide $ 107 $ by $ \color{blue}{ 35 } $ and get the remainder

$$ 107 : 35 = 3 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 11 :
Divide $ 35 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 35 : 2 = 17 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 12 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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