Step 1 :
Divide $ 15430 $ by $ 10430 $ and get the remainder

$$ 15430 : 10430 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10430 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10430 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 430 } \text{ ) } $$

The remainder is still positive ($ 430 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 430 } $ and get the remainder

$$ 5000 : 430 = 11 \text{ ( remainder is } \color{blue}{ 270 } \text{ ) } $$

The remainder is still positive ($ 270 > 0 $), so we will continue with division.

Step 4 :
Divide $ 430 $ by $ \color{blue}{ 270 } $ and get the remainder

$$ 430 : 270 = 1 \text{ ( remainder is } \color{blue}{ 160 } \text{ ) } $$

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

Step 5 :
Divide $ 270 $ by $ \color{blue}{ 160 } $ and get the remainder

$$ 270 : 160 = 1 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

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

Step 6 :
Divide $ 160 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 160 : 110 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is still positive ($ 50 > 0 $), so we will continue with division.

Step 7 :
Divide $ 110 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 110 : 50 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
Divide $ 50 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 50 : \color{blue}{ \boxed { 10 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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