Step 1 :
Divide $ 38675 $ by $ 24843 $ and get the remainder

$$ 38675 : 24843 = 1 \text{ ( remainder is } \color{blue}{ 13832 } \text{ ) } $$

The remainder is positive ($ 13832 > 0 $), so we will continue with division.

Step 2 :
Divide $ 24843 $ by $ \color{blue}{ 13832 } $ and get the remainder

$$ 24843 : 13832 = 1 \text{ ( remainder is } \color{blue}{ 11011 } \text{ ) } $$

The remainder is still positive ($ 11011 > 0 $), so we will continue with division.

Step 3 :
Divide $ 13832 $ by $ \color{blue}{ 11011 } $ and get the remainder

$$ 13832 : 11011 = 1 \text{ ( remainder is } \color{blue}{ 2821 } \text{ ) } $$

The remainder is still positive ($ 2821 > 0 $), so we will continue with division.

Step 4 :
Divide $ 11011 $ by $ \color{blue}{ 2821 } $ and get the remainder

$$ 11011 : 2821 = 3 \text{ ( remainder is } \color{blue}{ 2548 } \text{ ) } $$

The remainder is still positive ($ 2548 > 0 $), so we will continue with division.

Step 5 :
Divide $ 2821 $ by $ \color{blue}{ 2548 } $ and get the remainder

$$ 2821 : 2548 = 1 \text{ ( remainder is } \color{blue}{ 273 } \text{ ) } $$

The remainder is still positive ($ 273 > 0 $), so we will continue with division.

Step 6 :
Divide $ 2548 $ by $ \color{blue}{ 273 } $ and get the remainder

$$ 2548 : 273 = 9 \text{ ( remainder is } \color{blue}{ 91 } \text{ ) } $$

The remainder is still positive ($ 91 > 0 $), so we will continue with division.

Step 7 :
Divide $ 273 $ by $ \color{blue}{ 91 } $ and get the remainder

$$ 273 : \color{blue}{ \boxed { 91 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 91 }} $.

This solution can be visualized using a Venn diagram.

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

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