Step 1 :
Divide $ 3568 $ by $ 1601 $ and get the remainder

$$ 3568 : 1601 = 2 \text{ ( remainder is } \color{blue}{ 366 } \text{ ) } $$

The remainder is positive ($ 366 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1601 $ by $ \color{blue}{ 366 } $ and get the remainder

$$ 1601 : 366 = 4 \text{ ( remainder is } \color{blue}{ 137 } \text{ ) } $$

The remainder is still positive ($ 137 > 0 $), so we will continue with division.

Step 3 :
Divide $ 366 $ by $ \color{blue}{ 137 } $ and get the remainder

$$ 366 : 137 = 2 \text{ ( remainder is } \color{blue}{ 92 } \text{ ) } $$

The remainder is still positive ($ 92 > 0 $), so we will continue with division.

Step 4 :
Divide $ 137 $ by $ \color{blue}{ 92 } $ and get the remainder

$$ 137 : 92 = 1 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is still positive ($ 45 > 0 $), so we will continue with division.

Step 5 :
Divide $ 92 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 92 : 45 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 6 :
Divide $ 45 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 45 : 2 = 22 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
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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