Step 1 :
Divide $ 1611 $ by $ 627 $ and get the remainder

$$ 1611 : 627 = 2 \text{ ( remainder is } \color{blue}{ 357 } \text{ ) } $$

The remainder is positive ($ 357 > 0 $), so we will continue with division.

Step 2 :
Divide $ 627 $ by $ \color{blue}{ 357 } $ and get the remainder

$$ 627 : 357 = 1 \text{ ( remainder is } \color{blue}{ 270 } \text{ ) } $$

The remainder is still positive ($ 270 > 0 $), so we will continue with division.

Step 3 :
Divide $ 357 $ by $ \color{blue}{ 270 } $ and get the remainder

$$ 357 : 270 = 1 \text{ ( remainder is } \color{blue}{ 87 } \text{ ) } $$

The remainder is still positive ($ 87 > 0 $), so we will continue with division.

Step 4 :
Divide $ 270 $ by $ \color{blue}{ 87 } $ and get the remainder

$$ 270 : 87 = 3 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 5 :
Divide $ 87 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 87 : 9 = 9 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

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

$$ 9 : 6 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 7 :
Divide $ 6 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 3 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

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