Step 1 :
Divide $ 12870 $ by $ 2618 $ and get the remainder

$$ 12870 : 2618 = 4 \text{ ( remainder is } \color{blue}{ 2398 } \text{ ) } $$

The remainder is positive ($ 2398 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2618 $ by $ \color{blue}{ 2398 } $ and get the remainder

$$ 2618 : 2398 = 1 \text{ ( remainder is } \color{blue}{ 220 } \text{ ) } $$

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

Step 3 :
Divide $ 2398 $ by $ \color{blue}{ 220 } $ and get the remainder

$$ 2398 : 220 = 10 \text{ ( remainder is } \color{blue}{ 198 } \text{ ) } $$

The remainder is still positive ($ 198 > 0 $), so we will continue with division.

Step 4 :
Divide $ 220 $ by $ \color{blue}{ 198 } $ and get the remainder

$$ 220 : 198 = 1 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 5 :
Divide $ 198 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 198 : \color{blue}{ \boxed { 22 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 22 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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