Step 1 :
Divide $ 9989 $ by $ 2133 $ and get the remainder

$$ 9989 : 2133 = 4 \text{ ( remainder is } \color{blue}{ 1457 } \text{ ) } $$

The remainder is positive ($ 1457 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2133 $ by $ \color{blue}{ 1457 } $ and get the remainder

$$ 2133 : 1457 = 1 \text{ ( remainder is } \color{blue}{ 676 } \text{ ) } $$

The remainder is still positive ($ 676 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1457 $ by $ \color{blue}{ 676 } $ and get the remainder

$$ 1457 : 676 = 2 \text{ ( remainder is } \color{blue}{ 105 } \text{ ) } $$

The remainder is still positive ($ 105 > 0 $), so we will continue with division.

Step 4 :
Divide $ 676 $ by $ \color{blue}{ 105 } $ and get the remainder

$$ 676 : 105 = 6 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 5 :
Divide $ 105 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 105 : 46 = 2 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 6 :
Divide $ 46 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 46 : 13 = 3 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 7 :
Divide $ 13 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 13 : 7 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

Step 8 :
Divide $ 7 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 7 : 6 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 9 :
Divide $ 6 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 1 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator