Step 1 :
Divide $ 18430 $ by $ 13430 $ and get the remainder

$$ 18430 : 13430 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

The remainder is positive ($ 5000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 13430 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13430 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3430 } \text{ ) } $$

The remainder is still positive ($ 3430 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3430 } $ and get the remainder

$$ 5000 : 3430 = 1 \text{ ( remainder is } \color{blue}{ 1570 } \text{ ) } $$

The remainder is still positive ($ 1570 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3430 $ by $ \color{blue}{ 1570 } $ and get the remainder

$$ 3430 : 1570 = 2 \text{ ( remainder is } \color{blue}{ 290 } \text{ ) } $$

The remainder is still positive ($ 290 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1570 $ by $ \color{blue}{ 290 } $ and get the remainder

$$ 1570 : 290 = 5 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

The remainder is still positive ($ 120 > 0 $), so we will continue with division.

Step 6 :
Divide $ 290 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 290 : 120 = 2 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is still positive ($ 50 > 0 $), so we will continue with division.

Step 7 :
Divide $ 120 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 120 : 50 = 2 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 8 :
Divide $ 50 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 50 : 20 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 9 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 20 : \color{blue}{ \boxed { 10 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator