Step 1 :
Divide $ 18410 $ by $ 13410 $ and get the remainder

$$ 18410 : 13410 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13410 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13410 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3410 } \text{ ) } $$

The remainder is still positive ($ 3410 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3410 } $ and get the remainder

$$ 5000 : 3410 = 1 \text{ ( remainder is } \color{blue}{ 1590 } \text{ ) } $$

The remainder is still positive ($ 1590 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3410 $ by $ \color{blue}{ 1590 } $ and get the remainder

$$ 3410 : 1590 = 2 \text{ ( remainder is } \color{blue}{ 230 } \text{ ) } $$

The remainder is still positive ($ 230 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1590 $ by $ \color{blue}{ 230 } $ and get the remainder

$$ 1590 : 230 = 6 \text{ ( remainder is } \color{blue}{ 210 } \text{ ) } $$

The remainder is still positive ($ 210 > 0 $), so we will continue with division.

Step 6 :
Divide $ 230 $ by $ \color{blue}{ 210 } $ and get the remainder

$$ 230 : 210 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

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

Step 7 :
Divide $ 210 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 210 : 20 = 10 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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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