Step 1 :
Divide $ 34782 $ by $ 20119 $ and get the remainder

$$ 34782 : 20119 = 1 \text{ ( remainder is } \color{blue}{ 14663 } \text{ ) } $$

The remainder is positive ($ 14663 > 0 $), so we will continue with division.

Step 2 :
Divide $ 20119 $ by $ \color{blue}{ 14663 } $ and get the remainder

$$ 20119 : 14663 = 1 \text{ ( remainder is } \color{blue}{ 5456 } \text{ ) } $$

The remainder is still positive ($ 5456 > 0 $), so we will continue with division.

Step 3 :
Divide $ 14663 $ by $ \color{blue}{ 5456 } $ and get the remainder

$$ 14663 : 5456 = 2 \text{ ( remainder is } \color{blue}{ 3751 } \text{ ) } $$

The remainder is still positive ($ 3751 > 0 $), so we will continue with division.

Step 4 :
Divide $ 5456 $ by $ \color{blue}{ 3751 } $ and get the remainder

$$ 5456 : 3751 = 1 \text{ ( remainder is } \color{blue}{ 1705 } \text{ ) } $$

The remainder is still positive ($ 1705 > 0 $), so we will continue with division.

Step 5 :
Divide $ 3751 $ by $ \color{blue}{ 1705 } $ and get the remainder

$$ 3751 : 1705 = 2 \text{ ( remainder is } \color{blue}{ 341 } \text{ ) } $$

The remainder is still positive ($ 341 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1705 $ by $ \color{blue}{ 341 } $ and get the remainder

$$ 1705 : \color{blue}{ \boxed { 341 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 341 }} $.

This solution can be visualized using a Venn diagram.

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

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