Step 1 :
Divide $ 1771 $ by $ 179 $ and get the remainder

$$ 1771 : 179 = 9 \text{ ( remainder is } \color{blue}{ 160 } \text{ ) } $$

The remainder is positive ($ 160 > 0 $), so we will continue with division.

Step 2 :
Divide $ 179 $ by $ \color{blue}{ 160 } $ and get the remainder

$$ 179 : 160 = 1 \text{ ( remainder is } \color{blue}{ 19 } \text{ ) } $$

The remainder is still positive ($ 19 > 0 $), so we will continue with division.

Step 3 :
Divide $ 160 $ by $ \color{blue}{ 19 } $ and get the remainder

$$ 160 : 19 = 8 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 4 :
Divide $ 19 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 19 : 8 = 2 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 5 :
Divide $ 8 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 8 : 3 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 6 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

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