Step 1 :
Divide $ 18370 $ by $ 13370 $ and get the remainder

$$ 18370 : 13370 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13370 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13370 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3370 } \text{ ) } $$

The remainder is still positive ($ 3370 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3370 } $ and get the remainder

$$ 5000 : 3370 = 1 \text{ ( remainder is } \color{blue}{ 1630 } \text{ ) } $$

The remainder is still positive ($ 1630 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3370 $ by $ \color{blue}{ 1630 } $ and get the remainder

$$ 3370 : 1630 = 2 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

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

Step 5 :
Divide $ 1630 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 1630 : 110 = 14 \text{ ( remainder is } \color{blue}{ 90 } \text{ ) } $$

The remainder is still positive ($ 90 > 0 $), so we will continue with division.

Step 6 :
Divide $ 110 $ by $ \color{blue}{ 90 } $ and get the remainder

$$ 110 : 90 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 7 :
Divide $ 90 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 90 : 20 = 4 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
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.

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