Step 1 :
Divide $ 3568 $ by $ 1004 $ and get the remainder

$$ 3568 : 1004 = 3 \text{ ( remainder is } \color{blue}{ 556 } \text{ ) } $$

The remainder is positive ($ 556 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1004 $ by $ \color{blue}{ 556 } $ and get the remainder

$$ 1004 : 556 = 1 \text{ ( remainder is } \color{blue}{ 448 } \text{ ) } $$

The remainder is still positive ($ 448 > 0 $), so we will continue with division.

Step 3 :
Divide $ 556 $ by $ \color{blue}{ 448 } $ and get the remainder

$$ 556 : 448 = 1 \text{ ( remainder is } \color{blue}{ 108 } \text{ ) } $$

The remainder is still positive ($ 108 > 0 $), so we will continue with division.

Step 4 :
Divide $ 448 $ by $ \color{blue}{ 108 } $ and get the remainder

$$ 448 : 108 = 4 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 5 :
Divide $ 108 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 108 : 16 = 6 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 6 :
Divide $ 16 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 16 : 12 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 7 :
Divide $ 12 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 12 : \color{blue}{ \boxed { 4 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.

This solution can be visualized using a Venn diagram.

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

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