Step 1 :
Divide $ 902 $ by $ 412 $ and get the remainder

$$ 902 : 412 = 2 \text{ ( remainder is } \color{blue}{ 78 } \text{ ) } $$

The remainder is positive ($ 78 > 0 $), so we will continue with division.

Step 2 :
Divide $ 412 $ by $ \color{blue}{ 78 } $ and get the remainder

$$ 412 : 78 = 5 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 3 :
Divide $ 78 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 78 : 22 = 3 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 4 :
Divide $ 22 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 22 : 12 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 5 :
Divide $ 12 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 12 : 10 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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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