Step 1 :
Divide $ 3027 $ by $ 110 $ and get the remainder

$$ 3027 : 110 = 27 \text{ ( remainder is } \color{blue}{ 57 } \text{ ) } $$

The remainder is positive ($ 57 > 0 $), so we will continue with division.

Step 2 :
Divide $ 110 $ by $ \color{blue}{ 57 } $ and get the remainder

$$ 110 : 57 = 1 \text{ ( remainder is } \color{blue}{ 53 } \text{ ) } $$

The remainder is still positive ($ 53 > 0 $), so we will continue with division.

Step 3 :
Divide $ 57 $ by $ \color{blue}{ 53 } $ and get the remainder

$$ 57 : 53 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 4 :
Divide $ 53 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 53 : 4 = 13 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 5 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 1 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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