Step 1 :
Divide $ 142766 $ by $ 1729 $ and get the remainder

$$ 142766 : 1729 = 82 \text{ ( remainder is } \color{blue}{ 988 } \text{ ) } $$

The remainder is positive ($ 988 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1729 $ by $ \color{blue}{ 988 } $ and get the remainder

$$ 1729 : 988 = 1 \text{ ( remainder is } \color{blue}{ 741 } \text{ ) } $$

The remainder is still positive ($ 741 > 0 $), so we will continue with division.

Step 3 :
Divide $ 988 $ by $ \color{blue}{ 741 } $ and get the remainder

$$ 988 : 741 = 1 \text{ ( remainder is } \color{blue}{ 247 } \text{ ) } $$

The remainder is still positive ($ 247 > 0 $), so we will continue with division.

Step 4 :
Divide $ 741 $ by $ \color{blue}{ 247 } $ and get the remainder

$$ 741 : \color{blue}{ \boxed { 247 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 247 }} $.

This solution can be visualized using a Venn diagram.

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

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