Step 1 :
Divide $ 15730 $ by $ 10730 $ and get the remainder

$$ 15730 : 10730 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10730 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10730 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 730 } \text{ ) } $$

The remainder is still positive ($ 730 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 730 } $ and get the remainder

$$ 5000 : 730 = 6 \text{ ( remainder is } \color{blue}{ 620 } \text{ ) } $$

The remainder is still positive ($ 620 > 0 $), so we will continue with division.

Step 4 :
Divide $ 730 $ by $ \color{blue}{ 620 } $ and get the remainder

$$ 730 : 620 = 1 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

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

Step 5 :
Divide $ 620 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 620 : 110 = 5 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

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

Step 6 :
Divide $ 110 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 110 : 70 = 1 \text{ ( remainder is } \color{blue}{ 40 } \text{ ) } $$

The remainder is still positive ($ 40 > 0 $), so we will continue with division.

Step 7 :
Divide $ 70 $ by $ \color{blue}{ 40 } $ and get the remainder

$$ 70 : 40 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 8 :
Divide $ 40 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 40 : 30 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 9 :
Divide $ 30 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 30 : \color{blue}{ \boxed { 10 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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