Step 1 :
Divide $ 202851 $ by $ 22773 $ and get the remainder

$$ 202851 : 22773 = 8 \text{ ( remainder is } \color{blue}{ 20667 } \text{ ) } $$

The remainder is positive ($ 20667 > 0 $), so we will continue with division.

Step 2 :
Divide $ 22773 $ by $ \color{blue}{ 20667 } $ and get the remainder

$$ 22773 : 20667 = 1 \text{ ( remainder is } \color{blue}{ 2106 } \text{ ) } $$

The remainder is still positive ($ 2106 > 0 $), so we will continue with division.

Step 3 :
Divide $ 20667 $ by $ \color{blue}{ 2106 } $ and get the remainder

$$ 20667 : 2106 = 9 \text{ ( remainder is } \color{blue}{ 1713 } \text{ ) } $$

The remainder is still positive ($ 1713 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2106 $ by $ \color{blue}{ 1713 } $ and get the remainder

$$ 2106 : 1713 = 1 \text{ ( remainder is } \color{blue}{ 393 } \text{ ) } $$

The remainder is still positive ($ 393 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1713 $ by $ \color{blue}{ 393 } $ and get the remainder

$$ 1713 : 393 = 4 \text{ ( remainder is } \color{blue}{ 141 } \text{ ) } $$

The remainder is still positive ($ 141 > 0 $), so we will continue with division.

Step 6 :
Divide $ 393 $ by $ \color{blue}{ 141 } $ and get the remainder

$$ 393 : 141 = 2 \text{ ( remainder is } \color{blue}{ 111 } \text{ ) } $$

The remainder is still positive ($ 111 > 0 $), so we will continue with division.

Step 7 :
Divide $ 141 $ by $ \color{blue}{ 111 } $ and get the remainder

$$ 141 : 111 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 8 :
Divide $ 111 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 111 : 30 = 3 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 9 :
Divide $ 30 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 30 : 21 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 10 :
Divide $ 21 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 21 : 9 = 2 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 11 :
Divide $ 9 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 9 : \color{blue}{ \boxed { 3 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

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