Step 1 :
Divide $ 16410 $ by $ 11410 $ and get the remainder

$$ 16410 : 11410 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11410 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11410 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1410 } \text{ ) } $$

The remainder is still positive ($ 1410 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1410 } $ and get the remainder

$$ 5000 : 1410 = 3 \text{ ( remainder is } \color{blue}{ 770 } \text{ ) } $$

The remainder is still positive ($ 770 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1410 $ by $ \color{blue}{ 770 } $ and get the remainder

$$ 1410 : 770 = 1 \text{ ( remainder is } \color{blue}{ 640 } \text{ ) } $$

The remainder is still positive ($ 640 > 0 $), so we will continue with division.

Step 5 :
Divide $ 770 $ by $ \color{blue}{ 640 } $ and get the remainder

$$ 770 : 640 = 1 \text{ ( remainder is } \color{blue}{ 130 } \text{ ) } $$

The remainder is still positive ($ 130 > 0 $), so we will continue with division.

Step 6 :
Divide $ 640 $ by $ \color{blue}{ 130 } $ and get the remainder

$$ 640 : 130 = 4 \text{ ( remainder is } \color{blue}{ 120 } \text{ ) } $$

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

Step 7 :
Divide $ 130 $ by $ \color{blue}{ 120 } $ and get the remainder

$$ 130 : 120 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
Divide $ 120 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 120 : \color{blue}{ \boxed { 10 }} = 12 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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