Step 1 :
Divide $ 15870 $ by $ 10870 $ and get the remainder

$$ 15870 : 10870 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 10870 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10870 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 870 } \text{ ) } $$

The remainder is still positive ($ 870 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 870 } $ and get the remainder

$$ 5000 : 870 = 5 \text{ ( remainder is } \color{blue}{ 650 } \text{ ) } $$

The remainder is still positive ($ 650 > 0 $), so we will continue with division.

Step 4 :
Divide $ 870 $ by $ \color{blue}{ 650 } $ and get the remainder

$$ 870 : 650 = 1 \text{ ( remainder is } \color{blue}{ 220 } \text{ ) } $$

The remainder is still positive ($ 220 > 0 $), so we will continue with division.

Step 5 :
Divide $ 650 $ by $ \color{blue}{ 220 } $ and get the remainder

$$ 650 : 220 = 2 \text{ ( remainder is } \color{blue}{ 210 } \text{ ) } $$

The remainder is still positive ($ 210 > 0 $), so we will continue with division.

Step 6 :
Divide $ 220 $ by $ \color{blue}{ 210 } $ and get the remainder

$$ 220 : 210 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 7 :
Divide $ 210 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 210 : \color{blue}{ \boxed { 10 }} = 21 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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