Step 1 :
Divide $ 3810 $ by $ 417 $ and get the remainder

$$ 3810 : 417 = 9 \text{ ( remainder is } \color{blue}{ 57 } \text{ ) } $$

The remainder is positive ($ 57 > 0 $), so we will continue with division.

Step 2 :
Divide $ 417 $ by $ \color{blue}{ 57 } $ and get the remainder

$$ 417 : 57 = 7 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

The remainder is still positive ($ 18 > 0 $), so we will continue with division.

Step 3 :
Divide $ 57 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 57 : 18 = 3 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 4 :
Divide $ 18 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 18 : \color{blue}{ \boxed { 3 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

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