Step 1 :
Divide $ 4999 $ by $ 1109 $ and get the remainder

$$ 4999 : 1109 = 4 \text{ ( remainder is } \color{blue}{ 563 } \text{ ) } $$

The remainder is positive ($ 563 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1109 $ by $ \color{blue}{ 563 } $ and get the remainder

$$ 1109 : 563 = 1 \text{ ( remainder is } \color{blue}{ 546 } \text{ ) } $$

The remainder is still positive ($ 546 > 0 $), so we will continue with division.

Step 3 :
Divide $ 563 $ by $ \color{blue}{ 546 } $ and get the remainder

$$ 563 : 546 = 1 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 4 :
Divide $ 546 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 546 : 17 = 32 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 5 :
Divide $ 17 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 17 : 2 = 8 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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