Step 1 :
Divide $ 1937 $ by $ 1586 $ and get the remainder

$$ 1937 : 1586 = 1 \text{ ( remainder is } \color{blue}{ 351 } \text{ ) } $$

The remainder is positive ($ 351 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1586 $ by $ \color{blue}{ 351 } $ and get the remainder

$$ 1586 : 351 = 4 \text{ ( remainder is } \color{blue}{ 182 } \text{ ) } $$

The remainder is still positive ($ 182 > 0 $), so we will continue with division.

Step 3 :
Divide $ 351 $ by $ \color{blue}{ 182 } $ and get the remainder

$$ 351 : 182 = 1 \text{ ( remainder is } \color{blue}{ 169 } \text{ ) } $$

The remainder is still positive ($ 169 > 0 $), so we will continue with division.

Step 4 :
Divide $ 182 $ by $ \color{blue}{ 169 } $ and get the remainder

$$ 182 : 169 = 1 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 5 :
Divide $ 169 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 169 : \color{blue}{ \boxed { 13 }} = 13 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 13 }} $.

This solution can be visualized using a Venn diagram.

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

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