Step 1 :
Divide $ 277 $ by $ 143 $ and get the remainder

$$ 277 : 143 = 1 \text{ ( remainder is } \color{blue}{ 134 } \text{ ) } $$

The remainder is positive ($ 134 > 0 $), so we will continue with division.

Step 2 :
Divide $ 143 $ by $ \color{blue}{ 134 } $ and get the remainder

$$ 143 : 134 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

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

Step 3 :
Divide $ 134 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 134 : 9 = 14 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

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

Step 4 :
Divide $ 9 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 9 : 8 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 5 :
Divide $ 8 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 8 : \color{blue}{ \boxed { 1 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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