Step 1 :
Divide $ 22086 $ by $ 9990 $ and get the remainder

$$ 22086 : 9990 = 2 \text{ ( remainder is } \color{blue}{ 2106 } \text{ ) } $$

The remainder is positive ($ 2106 > 0 $), so we will continue with division.

Step 2 :
Divide $ 9990 $ by $ \color{blue}{ 2106 } $ and get the remainder

$$ 9990 : 2106 = 4 \text{ ( remainder is } \color{blue}{ 1566 } \text{ ) } $$

The remainder is still positive ($ 1566 > 0 $), so we will continue with division.

Step 3 :
Divide $ 2106 $ by $ \color{blue}{ 1566 } $ and get the remainder

$$ 2106 : 1566 = 1 \text{ ( remainder is } \color{blue}{ 540 } \text{ ) } $$

The remainder is still positive ($ 540 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1566 $ by $ \color{blue}{ 540 } $ and get the remainder

$$ 1566 : 540 = 2 \text{ ( remainder is } \color{blue}{ 486 } \text{ ) } $$

The remainder is still positive ($ 486 > 0 $), so we will continue with division.

Step 5 :
Divide $ 540 $ by $ \color{blue}{ 486 } $ and get the remainder

$$ 540 : 486 = 1 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

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

Step 6 :
Divide $ 486 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 486 : \color{blue}{ \boxed { 54 }} = 9 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 54 }} $.

This solution can be visualized using a Venn diagram.

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

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