Step 1 :
Divide $ 18470 $ by $ 13470 $ and get the remainder

$$ 18470 : 13470 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13470 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13470 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3470 } \text{ ) } $$

The remainder is still positive ($ 3470 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3470 } $ and get the remainder

$$ 5000 : 3470 = 1 \text{ ( remainder is } \color{blue}{ 1530 } \text{ ) } $$

The remainder is still positive ($ 1530 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3470 $ by $ \color{blue}{ 1530 } $ and get the remainder

$$ 3470 : 1530 = 2 \text{ ( remainder is } \color{blue}{ 410 } \text{ ) } $$

The remainder is still positive ($ 410 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1530 $ by $ \color{blue}{ 410 } $ and get the remainder

$$ 1530 : 410 = 3 \text{ ( remainder is } \color{blue}{ 300 } \text{ ) } $$

The remainder is still positive ($ 300 > 0 $), so we will continue with division.

Step 6 :
Divide $ 410 $ by $ \color{blue}{ 300 } $ and get the remainder

$$ 410 : 300 = 1 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

The remainder is still positive ($ 110 > 0 $), so we will continue with division.

Step 7 :
Divide $ 300 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 300 : 110 = 2 \text{ ( remainder is } \color{blue}{ 80 } \text{ ) } $$

The remainder is still positive ($ 80 > 0 $), so we will continue with division.

Step 8 :
Divide $ 110 $ by $ \color{blue}{ 80 } $ and get the remainder

$$ 110 : 80 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 9 :
Divide $ 80 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 80 : 30 = 2 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 10 :
Divide $ 30 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 30 : 20 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 11 :
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