Step 1 :
Divide $ 81719 $ by $ 52003 $ and get the remainder

$$ 81719 : 52003 = 1 \text{ ( remainder is } \color{blue}{ 29716 } \text{ ) } $$

The remainder is positive ($ 29716 > 0 $), so we will continue with division.

Step 2 :
Divide $ 52003 $ by $ \color{blue}{ 29716 } $ and get the remainder

$$ 52003 : 29716 = 1 \text{ ( remainder is } \color{blue}{ 22287 } \text{ ) } $$

The remainder is still positive ($ 22287 > 0 $), so we will continue with division.

Step 3 :
Divide $ 29716 $ by $ \color{blue}{ 22287 } $ and get the remainder

$$ 29716 : 22287 = 1 \text{ ( remainder is } \color{blue}{ 7429 } \text{ ) } $$

The remainder is still positive ($ 7429 > 0 $), so we will continue with division.

Step 4 :
Divide $ 22287 $ by $ \color{blue}{ 7429 } $ and get the remainder

$$ 22287 : \color{blue}{ \boxed { 7429 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7429 }} $.

This solution can be visualized using a Venn diagram.

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

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