Step 1 :
Divide $ 17830 $ by $ 12830 $ and get the remainder

$$ 17830 : 12830 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 12830 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 12830 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 2830 } \text{ ) } $$

The remainder is still positive ($ 2830 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 2830 } $ and get the remainder

$$ 5000 : 2830 = 1 \text{ ( remainder is } \color{blue}{ 2170 } \text{ ) } $$

The remainder is still positive ($ 2170 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2830 $ by $ \color{blue}{ 2170 } $ and get the remainder

$$ 2830 : 2170 = 1 \text{ ( remainder is } \color{blue}{ 660 } \text{ ) } $$

The remainder is still positive ($ 660 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2170 $ by $ \color{blue}{ 660 } $ and get the remainder

$$ 2170 : 660 = 3 \text{ ( remainder is } \color{blue}{ 190 } \text{ ) } $$

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

Step 6 :
Divide $ 660 $ by $ \color{blue}{ 190 } $ and get the remainder

$$ 660 : 190 = 3 \text{ ( remainder is } \color{blue}{ 90 } \text{ ) } $$

The remainder is still positive ($ 90 > 0 $), so we will continue with division.

Step 7 :
Divide $ 190 $ by $ \color{blue}{ 90 } $ and get the remainder

$$ 190 : 90 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
Divide $ 90 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 90 : \color{blue}{ \boxed { 10 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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