Step 1 :
Divide $ 2260 $ by $ 812 $ and get the remainder

$$ 2260 : 812 = 2 \text{ ( remainder is } \color{blue}{ 636 } \text{ ) } $$

The remainder is positive ($ 636 > 0 $), so we will continue with division.

Step 2 :
Divide $ 812 $ by $ \color{blue}{ 636 } $ and get the remainder

$$ 812 : 636 = 1 \text{ ( remainder is } \color{blue}{ 176 } \text{ ) } $$

The remainder is still positive ($ 176 > 0 $), so we will continue with division.

Step 3 :
Divide $ 636 $ by $ \color{blue}{ 176 } $ and get the remainder

$$ 636 : 176 = 3 \text{ ( remainder is } \color{blue}{ 108 } \text{ ) } $$

The remainder is still positive ($ 108 > 0 $), so we will continue with division.

Step 4 :
Divide $ 176 $ by $ \color{blue}{ 108 } $ and get the remainder

$$ 176 : 108 = 1 \text{ ( remainder is } \color{blue}{ 68 } \text{ ) } $$

The remainder is still positive ($ 68 > 0 $), so we will continue with division.

Step 5 :
Divide $ 108 $ by $ \color{blue}{ 68 } $ and get the remainder

$$ 108 : 68 = 1 \text{ ( remainder is } \color{blue}{ 40 } \text{ ) } $$

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

Step 6 :
Divide $ 68 $ by $ \color{blue}{ 40 } $ and get the remainder

$$ 68 : 40 = 1 \text{ ( remainder is } \color{blue}{ 28 } \text{ ) } $$

The remainder is still positive ($ 28 > 0 $), so we will continue with division.

Step 7 :
Divide $ 40 $ by $ \color{blue}{ 28 } $ and get the remainder

$$ 40 : 28 = 1 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

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

Step 8 :
Divide $ 28 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 28 : 12 = 2 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 9 :
Divide $ 12 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 12 : \color{blue}{ \boxed { 4 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.

This solution can be visualized using a Venn diagram.

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

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