Step 1 :
Divide $ 1664972998 $ by $ 1107550223 $ and get the remainder

$$ 1664972998 : 1107550223 = 1 \text{ ( remainder is } \color{blue}{ 557422775 } \text{ ) } $$

The remainder is positive ($ 557422775 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1107550223 $ by $ \color{blue}{ 557422775 } $ and get the remainder

$$ 1107550223 : 557422775 = 1 \text{ ( remainder is } \color{blue}{ 550127448 } \text{ ) } $$

The remainder is still positive ($ 550127448 > 0 $), so we will continue with division.

Step 3 :
Divide $ 557422775 $ by $ \color{blue}{ 550127448 } $ and get the remainder

$$ 557422775 : 550127448 = 1 \text{ ( remainder is } \color{blue}{ 7295327 } \text{ ) } $$

The remainder is still positive ($ 7295327 > 0 $), so we will continue with division.

Step 4 :
Divide $ 550127448 $ by $ \color{blue}{ 7295327 } $ and get the remainder

$$ 550127448 : 7295327 = 75 \text{ ( remainder is } \color{blue}{ 2977923 } \text{ ) } $$

The remainder is still positive ($ 2977923 > 0 $), so we will continue with division.

Step 5 :
Divide $ 7295327 $ by $ \color{blue}{ 2977923 } $ and get the remainder

$$ 7295327 : 2977923 = 2 \text{ ( remainder is } \color{blue}{ 1339481 } \text{ ) } $$

The remainder is still positive ($ 1339481 > 0 $), so we will continue with division.

Step 6 :
Divide $ 2977923 $ by $ \color{blue}{ 1339481 } $ and get the remainder

$$ 2977923 : 1339481 = 2 \text{ ( remainder is } \color{blue}{ 298961 } \text{ ) } $$

The remainder is still positive ($ 298961 > 0 $), so we will continue with division.

Step 7 :
Divide $ 1339481 $ by $ \color{blue}{ 298961 } $ and get the remainder

$$ 1339481 : 298961 = 4 \text{ ( remainder is } \color{blue}{ 143637 } \text{ ) } $$

The remainder is still positive ($ 143637 > 0 $), so we will continue with division.

Step 8 :
Divide $ 298961 $ by $ \color{blue}{ 143637 } $ and get the remainder

$$ 298961 : 143637 = 2 \text{ ( remainder is } \color{blue}{ 11687 } \text{ ) } $$

The remainder is still positive ($ 11687 > 0 $), so we will continue with division.

Step 9 :
Divide $ 143637 $ by $ \color{blue}{ 11687 } $ and get the remainder

$$ 143637 : 11687 = 12 \text{ ( remainder is } \color{blue}{ 3393 } \text{ ) } $$

The remainder is still positive ($ 3393 > 0 $), so we will continue with division.

Step 10 :
Divide $ 11687 $ by $ \color{blue}{ 3393 } $ and get the remainder

$$ 11687 : 3393 = 3 \text{ ( remainder is } \color{blue}{ 1508 } \text{ ) } $$

The remainder is still positive ($ 1508 > 0 $), so we will continue with division.

Step 11 :
Divide $ 3393 $ by $ \color{blue}{ 1508 } $ and get the remainder

$$ 3393 : 1508 = 2 \text{ ( remainder is } \color{blue}{ 377 } \text{ ) } $$

The remainder is still positive ($ 377 > 0 $), so we will continue with division.

Step 12 :
Divide $ 1508 $ by $ \color{blue}{ 377 } $ and get the remainder

$$ 1508 : \color{blue}{ \boxed { 377 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 377 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator