Step 1 :
Divide $ 500 $ by $ 193 $ and get the remainder

$$ 500 : 193 = 2 \text{ ( remainder is } \color{blue}{ 114 } \text{ ) } $$

The remainder is positive ($ 114 > 0 $), so we will continue with division.

Step 2 :
Divide $ 193 $ by $ \color{blue}{ 114 } $ and get the remainder

$$ 193 : 114 = 1 \text{ ( remainder is } \color{blue}{ 79 } \text{ ) } $$

The remainder is still positive ($ 79 > 0 $), so we will continue with division.

Step 3 :
Divide $ 114 $ by $ \color{blue}{ 79 } $ and get the remainder

$$ 114 : 79 = 1 \text{ ( remainder is } \color{blue}{ 35 } \text{ ) } $$

The remainder is still positive ($ 35 > 0 $), so we will continue with division.

Step 4 :
Divide $ 79 $ by $ \color{blue}{ 35 } $ and get the remainder

$$ 79 : 35 = 2 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 35 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 35 : 9 = 3 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

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

Step 6 :
Divide $ 9 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 9 : 8 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 8 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 8 : \color{blue}{ \boxed { 1 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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