Step 1 :
Divide $ 17530 $ by $ 12530 $ and get the remainder

$$ 17530 : 12530 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 12530 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 12530 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 2530 } \text{ ) } $$

The remainder is still positive ($ 2530 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 2530 } $ and get the remainder

$$ 5000 : 2530 = 1 \text{ ( remainder is } \color{blue}{ 2470 } \text{ ) } $$

The remainder is still positive ($ 2470 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2530 $ by $ \color{blue}{ 2470 } $ and get the remainder

$$ 2530 : 2470 = 1 \text{ ( remainder is } \color{blue}{ 60 } \text{ ) } $$

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

Step 5 :
Divide $ 2470 $ by $ \color{blue}{ 60 } $ and get the remainder

$$ 2470 : 60 = 41 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 6 :
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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