Step 1 :
Divide $ 15370 $ by $ 10370 $ and get the remainder

$$ 15370 : 10370 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10370 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10370 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 370 } \text{ ) } $$

The remainder is still positive ($ 370 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 370 } $ and get the remainder

$$ 5000 : 370 = 13 \text{ ( remainder is } \color{blue}{ 190 } \text{ ) } $$

The remainder is still positive ($ 190 > 0 $), so we will continue with division.

Step 4 :
Divide $ 370 $ by $ \color{blue}{ 190 } $ and get the remainder

$$ 370 : 190 = 1 \text{ ( remainder is } \color{blue}{ 180 } \text{ ) } $$

The remainder is still positive ($ 180 > 0 $), so we will continue with division.

Step 5 :
Divide $ 190 $ by $ \color{blue}{ 180 } $ and get the remainder

$$ 190 : 180 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 6 :
Divide $ 180 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 180 : \color{blue}{ \boxed { 10 }} = 18 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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