Step 1 :
Divide $ 98765 $ by $ 54321 $ and get the remainder

$$ 98765 : 54321 = 1 \text{ ( remainder is } \color{blue}{ 44444 } \text{ ) } $$

The remainder is positive ($ 44444 > 0 $), so we will continue with division.

Step 2 :
Divide $ 54321 $ by $ \color{blue}{ 44444 } $ and get the remainder

$$ 54321 : 44444 = 1 \text{ ( remainder is } \color{blue}{ 9877 } \text{ ) } $$

The remainder is still positive ($ 9877 > 0 $), so we will continue with division.

Step 3 :
Divide $ 44444 $ by $ \color{blue}{ 9877 } $ and get the remainder

$$ 44444 : 9877 = 4 \text{ ( remainder is } \color{blue}{ 4936 } \text{ ) } $$

The remainder is still positive ($ 4936 > 0 $), so we will continue with division.

Step 4 :
Divide $ 9877 $ by $ \color{blue}{ 4936 } $ and get the remainder

$$ 9877 : 4936 = 2 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

The remainder is still positive ($ 5 > 0 $), so we will continue with division.

Step 5 :
Divide $ 4936 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 4936 : 5 = 987 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 5 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 5 : \color{blue}{ \boxed { 1 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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