Step 1 :
Divide $ 3962 $ by $ 1589 $ and get the remainder

$$ 3962 : 1589 = 2 \text{ ( remainder is } \color{blue}{ 784 } \text{ ) } $$

The remainder is positive ($ 784 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1589 $ by $ \color{blue}{ 784 } $ and get the remainder

$$ 1589 : 784 = 2 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 3 :
Divide $ 784 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 784 : 21 = 37 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 4 :
Divide $ 21 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 21 : \color{blue}{ \boxed { 7 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.

This solution can be visualized using a Venn diagram.

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

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