Step 1 :
Divide $ 4200021066 $ by $ 155590302 $ and get the remainder

$$ 4200021066 : 155590302 = 26 \text{ ( remainder is } \color{blue}{ 154673214 } \text{ ) } $$

The remainder is positive ($ 154673214 > 0 $), so we will continue with division.

Step 2 :
Divide $ 155590302 $ by $ \color{blue}{ 154673214 } $ and get the remainder

$$ 155590302 : 154673214 = 1 \text{ ( remainder is } \color{blue}{ 917088 } \text{ ) } $$

The remainder is still positive ($ 917088 > 0 $), so we will continue with division.

Step 3 :
Divide $ 154673214 $ by $ \color{blue}{ 917088 } $ and get the remainder

$$ 154673214 : 917088 = 168 \text{ ( remainder is } \color{blue}{ 602430 } \text{ ) } $$

The remainder is still positive ($ 602430 > 0 $), so we will continue with division.

Step 4 :
Divide $ 917088 $ by $ \color{blue}{ 602430 } $ and get the remainder

$$ 917088 : 602430 = 1 \text{ ( remainder is } \color{blue}{ 314658 } \text{ ) } $$

The remainder is still positive ($ 314658 > 0 $), so we will continue with division.

Step 5 :
Divide $ 602430 $ by $ \color{blue}{ 314658 } $ and get the remainder

$$ 602430 : 314658 = 1 \text{ ( remainder is } \color{blue}{ 287772 } \text{ ) } $$

The remainder is still positive ($ 287772 > 0 $), so we will continue with division.

Step 6 :
Divide $ 314658 $ by $ \color{blue}{ 287772 } $ and get the remainder

$$ 314658 : 287772 = 1 \text{ ( remainder is } \color{blue}{ 26886 } \text{ ) } $$

The remainder is still positive ($ 26886 > 0 $), so we will continue with division.

Step 7 :
Divide $ 287772 $ by $ \color{blue}{ 26886 } $ and get the remainder

$$ 287772 : 26886 = 10 \text{ ( remainder is } \color{blue}{ 18912 } \text{ ) } $$

The remainder is still positive ($ 18912 > 0 $), so we will continue with division.

Step 8 :
Divide $ 26886 $ by $ \color{blue}{ 18912 } $ and get the remainder

$$ 26886 : 18912 = 1 \text{ ( remainder is } \color{blue}{ 7974 } \text{ ) } $$

The remainder is still positive ($ 7974 > 0 $), so we will continue with division.

Step 9 :
Divide $ 18912 $ by $ \color{blue}{ 7974 } $ and get the remainder

$$ 18912 : 7974 = 2 \text{ ( remainder is } \color{blue}{ 2964 } \text{ ) } $$

The remainder is still positive ($ 2964 > 0 $), so we will continue with division.

Step 10 :
Divide $ 7974 $ by $ \color{blue}{ 2964 } $ and get the remainder

$$ 7974 : 2964 = 2 \text{ ( remainder is } \color{blue}{ 2046 } \text{ ) } $$

The remainder is still positive ($ 2046 > 0 $), so we will continue with division.

Step 11 :
Divide $ 2964 $ by $ \color{blue}{ 2046 } $ and get the remainder

$$ 2964 : 2046 = 1 \text{ ( remainder is } \color{blue}{ 918 } \text{ ) } $$

The remainder is still positive ($ 918 > 0 $), so we will continue with division.

Step 12 :
Divide $ 2046 $ by $ \color{blue}{ 918 } $ and get the remainder

$$ 2046 : 918 = 2 \text{ ( remainder is } \color{blue}{ 210 } \text{ ) } $$

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

Step 13 :
Divide $ 918 $ by $ \color{blue}{ 210 } $ and get the remainder

$$ 918 : 210 = 4 \text{ ( remainder is } \color{blue}{ 78 } \text{ ) } $$

The remainder is still positive ($ 78 > 0 $), so we will continue with division.

Step 14 :
Divide $ 210 $ by $ \color{blue}{ 78 } $ and get the remainder

$$ 210 : 78 = 2 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

The remainder is still positive ($ 54 > 0 $), so we will continue with division.

Step 15 :
Divide $ 78 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 78 : 54 = 1 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 16 :
Divide $ 54 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 54 : 24 = 2 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 17 :
Divide $ 24 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 24 : \color{blue}{ \boxed { 6 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator