Step 1 :
Divide $ 3512 $ by $ 888 $ and get the remainder

$$ 3512 : 888 = 3 \text{ ( remainder is } \color{blue}{ 848 } \text{ ) } $$

The remainder is positive ($ 848 > 0 $), so we will continue with division.

Step 2 :
Divide $ 888 $ by $ \color{blue}{ 848 } $ and get the remainder

$$ 888 : 848 = 1 \text{ ( remainder is } \color{blue}{ 40 } \text{ ) } $$

The remainder is still positive ($ 40 > 0 $), so we will continue with division.

Step 3 :
Divide $ 848 $ by $ \color{blue}{ 40 } $ and get the remainder

$$ 848 : 40 = 21 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 4 :
Divide $ 40 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 40 : \color{blue}{ \boxed { 8 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.

This solution can be visualized using a Venn diagram.

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

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