Step 1 :
Divide $ 629 $ by $ 335 $ and get the remainder

$$ 629 : 335 = 1 \text{ ( remainder is } \color{blue}{ 294 } \text{ ) } $$

The remainder is positive ($ 294 > 0 $), so we will continue with division.

Step 2 :
Divide $ 335 $ by $ \color{blue}{ 294 } $ and get the remainder

$$ 335 : 294 = 1 \text{ ( remainder is } \color{blue}{ 41 } \text{ ) } $$

The remainder is still positive ($ 41 > 0 $), so we will continue with division.

Step 3 :
Divide $ 294 $ by $ \color{blue}{ 41 } $ and get the remainder

$$ 294 : 41 = 7 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

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

Step 4 :
Divide $ 41 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 41 : 7 = 5 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 5 :
Divide $ 7 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 7 : 6 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 6 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 1 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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