Step 1 :
Divide $ 1391 $ by $ 563 $ and get the remainder

$$ 1391 : 563 = 2 \text{ ( remainder is } \color{blue}{ 265 } \text{ ) } $$

The remainder is positive ($ 265 > 0 $), so we will continue with division.

Step 2 :
Divide $ 563 $ by $ \color{blue}{ 265 } $ and get the remainder

$$ 563 : 265 = 2 \text{ ( remainder is } \color{blue}{ 33 } \text{ ) } $$

The remainder is still positive ($ 33 > 0 $), so we will continue with division.

Step 3 :
Divide $ 265 $ by $ \color{blue}{ 33 } $ and get the remainder

$$ 265 : 33 = 8 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 4 :
Divide $ 33 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 33 : \color{blue}{ \boxed { 1 }} = 33 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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