Step 1 :
Divide $ 10092 $ by $ 1654 $ and get the remainder

$$ 10092 : 1654 = 6 \text{ ( remainder is } \color{blue}{ 168 } \text{ ) } $$

The remainder is positive ($ 168 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1654 $ by $ \color{blue}{ 168 } $ and get the remainder

$$ 1654 : 168 = 9 \text{ ( remainder is } \color{blue}{ 142 } \text{ ) } $$

The remainder is still positive ($ 142 > 0 $), so we will continue with division.

Step 3 :
Divide $ 168 $ by $ \color{blue}{ 142 } $ and get the remainder

$$ 168 : 142 = 1 \text{ ( remainder is } \color{blue}{ 26 } \text{ ) } $$

The remainder is still positive ($ 26 > 0 $), so we will continue with division.

Step 4 :
Divide $ 142 $ by $ \color{blue}{ 26 } $ and get the remainder

$$ 142 : 26 = 5 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 5 :
Divide $ 26 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 26 : 12 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 6 :
Divide $ 12 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 12 : \color{blue}{ \boxed { 2 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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