Step 1 :
Divide $ 3126 $ by $ 1386 $ and get the remainder

$$ 3126 : 1386 = 2 \text{ ( remainder is } \color{blue}{ 354 } \text{ ) } $$

The remainder is positive ($ 354 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1386 $ by $ \color{blue}{ 354 } $ and get the remainder

$$ 1386 : 354 = 3 \text{ ( remainder is } \color{blue}{ 324 } \text{ ) } $$

The remainder is still positive ($ 324 > 0 $), so we will continue with division.

Step 3 :
Divide $ 354 $ by $ \color{blue}{ 324 } $ and get the remainder

$$ 354 : 324 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 4 :
Divide $ 324 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 324 : 30 = 10 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 5 :
Divide $ 30 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 30 : 24 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 6 :
Divide $ 24 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 24 : \color{blue}{ \boxed { 6 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.

This solution can be visualized using a Venn diagram.

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

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