Step 1 :
Divide $ 15530 $ by $ 10530 $ and get the remainder

$$ 15530 : 10530 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10530 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10530 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 530 } \text{ ) } $$

The remainder is still positive ($ 530 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 530 } $ and get the remainder

$$ 5000 : 530 = 9 \text{ ( remainder is } \color{blue}{ 230 } \text{ ) } $$

The remainder is still positive ($ 230 > 0 $), so we will continue with division.

Step 4 :
Divide $ 530 $ by $ \color{blue}{ 230 } $ and get the remainder

$$ 530 : 230 = 2 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

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

Step 5 :
Divide $ 230 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 230 : 70 = 3 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 6 :
Divide $ 70 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 70 : 20 = 3 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 7 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 20 : \color{blue}{ \boxed { 10 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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