Step 1 :
Divide $ 21829500 $ by $ 7871850 $ and get the remainder

$$ 21829500 : 7871850 = 2 \text{ ( remainder is } \color{blue}{ 6085800 } \text{ ) } $$

The remainder is positive ($ 6085800 > 0 $), so we will continue with division.

Step 2 :
Divide $ 7871850 $ by $ \color{blue}{ 6085800 } $ and get the remainder

$$ 7871850 : 6085800 = 1 \text{ ( remainder is } \color{blue}{ 1786050 } \text{ ) } $$

The remainder is still positive ($ 1786050 > 0 $), so we will continue with division.

Step 3 :
Divide $ 6085800 $ by $ \color{blue}{ 1786050 } $ and get the remainder

$$ 6085800 : 1786050 = 3 \text{ ( remainder is } \color{blue}{ 727650 } \text{ ) } $$

The remainder is still positive ($ 727650 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1786050 $ by $ \color{blue}{ 727650 } $ and get the remainder

$$ 1786050 : 727650 = 2 \text{ ( remainder is } \color{blue}{ 330750 } \text{ ) } $$

The remainder is still positive ($ 330750 > 0 $), so we will continue with division.

Step 5 :
Divide $ 727650 $ by $ \color{blue}{ 330750 } $ and get the remainder

$$ 727650 : 330750 = 2 \text{ ( remainder is } \color{blue}{ 66150 } \text{ ) } $$

The remainder is still positive ($ 66150 > 0 $), so we will continue with division.

Step 6 :
Divide $ 330750 $ by $ \color{blue}{ 66150 } $ and get the remainder

$$ 330750 : \color{blue}{ \boxed { 66150 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 66150 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator