Step 1 :
Divide $ 80 $ by $ 29 $ and get the remainder

$$ 80 : 29 = 2 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is positive ($ 22 > 0 $), so we will continue with division.

Step 2 :
Divide $ 29 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 29 : 22 = 1 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 3 :
Divide $ 22 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 22 : 7 = 3 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 4 :
Divide $ 7 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 7 : \color{blue}{ \boxed { 1 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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