Step 1 :
Divide $ 17930 $ by $ 12930 $ and get the remainder

$$ 17930 : 12930 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 12930 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 12930 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 2930 } \text{ ) } $$

The remainder is still positive ($ 2930 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 2930 } $ and get the remainder

$$ 5000 : 2930 = 1 \text{ ( remainder is } \color{blue}{ 2070 } \text{ ) } $$

The remainder is still positive ($ 2070 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2930 $ by $ \color{blue}{ 2070 } $ and get the remainder

$$ 2930 : 2070 = 1 \text{ ( remainder is } \color{blue}{ 860 } \text{ ) } $$

The remainder is still positive ($ 860 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2070 $ by $ \color{blue}{ 860 } $ and get the remainder

$$ 2070 : 860 = 2 \text{ ( remainder is } \color{blue}{ 350 } \text{ ) } $$

The remainder is still positive ($ 350 > 0 $), so we will continue with division.

Step 6 :
Divide $ 860 $ by $ \color{blue}{ 350 } $ and get the remainder

$$ 860 : 350 = 2 \text{ ( remainder is } \color{blue}{ 160 } \text{ ) } $$

The remainder is still positive ($ 160 > 0 $), so we will continue with division.

Step 7 :
Divide $ 350 $ by $ \color{blue}{ 160 } $ and get the remainder

$$ 350 : 160 = 2 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

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

Step 8 :
Divide $ 160 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 160 : 30 = 5 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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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