Step 1 :
Divide $ 5981 $ by $ 697 $ and get the remainder

$$ 5981 : 697 = 8 \text{ ( remainder is } \color{blue}{ 405 } \text{ ) } $$

The remainder is positive ($ 405 > 0 $), so we will continue with division.

Step 2 :
Divide $ 697 $ by $ \color{blue}{ 405 } $ and get the remainder

$$ 697 : 405 = 1 \text{ ( remainder is } \color{blue}{ 292 } \text{ ) } $$

The remainder is still positive ($ 292 > 0 $), so we will continue with division.

Step 3 :
Divide $ 405 $ by $ \color{blue}{ 292 } $ and get the remainder

$$ 405 : 292 = 1 \text{ ( remainder is } \color{blue}{ 113 } \text{ ) } $$

The remainder is still positive ($ 113 > 0 $), so we will continue with division.

Step 4 :
Divide $ 292 $ by $ \color{blue}{ 113 } $ and get the remainder

$$ 292 : 113 = 2 \text{ ( remainder is } \color{blue}{ 66 } \text{ ) } $$

The remainder is still positive ($ 66 > 0 $), so we will continue with division.

Step 5 :
Divide $ 113 $ by $ \color{blue}{ 66 } $ and get the remainder

$$ 113 : 66 = 1 \text{ ( remainder is } \color{blue}{ 47 } \text{ ) } $$

The remainder is still positive ($ 47 > 0 $), so we will continue with division.

Step 6 :
Divide $ 66 $ by $ \color{blue}{ 47 } $ and get the remainder

$$ 66 : 47 = 1 \text{ ( remainder is } \color{blue}{ 19 } \text{ ) } $$

The remainder is still positive ($ 19 > 0 $), so we will continue with division.

Step 7 :
Divide $ 47 $ by $ \color{blue}{ 19 } $ and get the remainder

$$ 47 : 19 = 2 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 8 :
Divide $ 19 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 19 : 9 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 9 :
Divide $ 9 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 9 : \color{blue}{ \boxed { 1 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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