Step 1 :
Divide $ 2772 $ by $ 1912 $ and get the remainder

$$ 2772 : 1912 = 1 \text{ ( remainder is } \color{blue}{ 860 } \text{ ) } $$

The remainder is positive ($ 860 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1912 $ by $ \color{blue}{ 860 } $ and get the remainder

$$ 1912 : 860 = 2 \text{ ( remainder is } \color{blue}{ 192 } \text{ ) } $$

The remainder is still positive ($ 192 > 0 $), so we will continue with division.

Step 3 :
Divide $ 860 $ by $ \color{blue}{ 192 } $ and get the remainder

$$ 860 : 192 = 4 \text{ ( remainder is } \color{blue}{ 92 } \text{ ) } $$

The remainder is still positive ($ 92 > 0 $), so we will continue with division.

Step 4 :
Divide $ 192 $ by $ \color{blue}{ 92 } $ and get the remainder

$$ 192 : 92 = 2 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

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

Step 5 :
Divide $ 92 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 92 : 8 = 11 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 6 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 8 : \color{blue}{ \boxed { 4 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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