Step 1 :
Divide $ 3512 $ by $ 856 $ and get the remainder

$$ 3512 : 856 = 4 \text{ ( remainder is } \color{blue}{ 88 } \text{ ) } $$

The remainder is positive ($ 88 > 0 $), so we will continue with division.

Step 2 :
Divide $ 856 $ by $ \color{blue}{ 88 } $ and get the remainder

$$ 856 : 88 = 9 \text{ ( remainder is } \color{blue}{ 64 } \text{ ) } $$

The remainder is still positive ($ 64 > 0 $), so we will continue with division.

Step 3 :
Divide $ 88 $ by $ \color{blue}{ 64 } $ and get the remainder

$$ 88 : 64 = 1 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

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

Step 4 :
Divide $ 64 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 64 : 24 = 2 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 5 :
Divide $ 24 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 24 : 16 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

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

Step 6 :
Divide $ 16 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 16 : \color{blue}{ \boxed { 8 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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