Step 1 :
Divide $ 3572 $ by $ 838 $ and get the remainder

$$ 3572 : 838 = 4 \text{ ( remainder is } \color{blue}{ 220 } \text{ ) } $$

The remainder is positive ($ 220 > 0 $), so we will continue with division.

Step 2 :
Divide $ 838 $ by $ \color{blue}{ 220 } $ and get the remainder

$$ 838 : 220 = 3 \text{ ( remainder is } \color{blue}{ 178 } \text{ ) } $$

The remainder is still positive ($ 178 > 0 $), so we will continue with division.

Step 3 :
Divide $ 220 $ by $ \color{blue}{ 178 } $ and get the remainder

$$ 220 : 178 = 1 \text{ ( remainder is } \color{blue}{ 42 } \text{ ) } $$

The remainder is still positive ($ 42 > 0 $), so we will continue with division.

Step 4 :
Divide $ 178 $ by $ \color{blue}{ 42 } $ and get the remainder

$$ 178 : 42 = 4 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 5 :
Divide $ 42 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 42 : 10 = 4 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 6 :
Divide $ 10 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 10 : \color{blue}{ \boxed { 2 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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