Step 1 :
Divide $ 2601 $ by $ 1836 $ and get the remainder

$$ 2601 : 1836 = 1 \text{ ( remainder is } \color{blue}{ 765 } \text{ ) } $$

The remainder is positive ($ 765 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1836 $ by $ \color{blue}{ 765 } $ and get the remainder

$$ 1836 : 765 = 2 \text{ ( remainder is } \color{blue}{ 306 } \text{ ) } $$

The remainder is still positive ($ 306 > 0 $), so we will continue with division.

Step 3 :
Divide $ 765 $ by $ \color{blue}{ 306 } $ and get the remainder

$$ 765 : 306 = 2 \text{ ( remainder is } \color{blue}{ 153 } \text{ ) } $$

The remainder is still positive ($ 153 > 0 $), so we will continue with division.

Step 4 :
Divide $ 306 $ by $ \color{blue}{ 153 } $ and get the remainder

$$ 306 : \color{blue}{ \boxed { 153 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 153 }} $.

This solution can be visualized using a Venn diagram.

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

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