Step 1 :
Divide $ 16370 $ by $ 11370 $ and get the remainder

$$ 16370 : 11370 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11370 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11370 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1370 } \text{ ) } $$

The remainder is still positive ($ 1370 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1370 } $ and get the remainder

$$ 5000 : 1370 = 3 \text{ ( remainder is } \color{blue}{ 890 } \text{ ) } $$

The remainder is still positive ($ 890 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1370 $ by $ \color{blue}{ 890 } $ and get the remainder

$$ 1370 : 890 = 1 \text{ ( remainder is } \color{blue}{ 480 } \text{ ) } $$

The remainder is still positive ($ 480 > 0 $), so we will continue with division.

Step 5 :
Divide $ 890 $ by $ \color{blue}{ 480 } $ and get the remainder

$$ 890 : 480 = 1 \text{ ( remainder is } \color{blue}{ 410 } \text{ ) } $$

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

Step 6 :
Divide $ 480 $ by $ \color{blue}{ 410 } $ and get the remainder

$$ 480 : 410 = 1 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 7 :
Divide $ 410 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 410 : 70 = 5 \text{ ( remainder is } \color{blue}{ 60 } \text{ ) } $$

The remainder is still positive ($ 60 > 0 $), so we will continue with division.

Step 8 :
Divide $ 70 $ by $ \color{blue}{ 60 } $ and get the remainder

$$ 70 : 60 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 9 :
Divide $ 60 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 60 : \color{blue}{ \boxed { 10 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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