Step 1 :
Divide $ 24601 $ by $ 1776 $ and get the remainder

$$ 24601 : 1776 = 13 \text{ ( remainder is } \color{blue}{ 1513 } \text{ ) } $$

The remainder is positive ($ 1513 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1776 $ by $ \color{blue}{ 1513 } $ and get the remainder

$$ 1776 : 1513 = 1 \text{ ( remainder is } \color{blue}{ 263 } \text{ ) } $$

The remainder is still positive ($ 263 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1513 $ by $ \color{blue}{ 263 } $ and get the remainder

$$ 1513 : 263 = 5 \text{ ( remainder is } \color{blue}{ 198 } \text{ ) } $$

The remainder is still positive ($ 198 > 0 $), so we will continue with division.

Step 4 :
Divide $ 263 $ by $ \color{blue}{ 198 } $ and get the remainder

$$ 263 : 198 = 1 \text{ ( remainder is } \color{blue}{ 65 } \text{ ) } $$

The remainder is still positive ($ 65 > 0 $), so we will continue with division.

Step 5 :
Divide $ 198 $ by $ \color{blue}{ 65 } $ and get the remainder

$$ 198 : 65 = 3 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 6 :
Divide $ 65 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 65 : 3 = 21 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 7 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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