Step 1 :
Divide $ 949509 $ by $ 74569 $ and get the remainder

$$ 949509 : 74569 = 12 \text{ ( remainder is } \color{blue}{ 54681 } \text{ ) } $$

The remainder is positive ($ 54681 > 0 $), so we will continue with division.

Step 2 :
Divide $ 74569 $ by $ \color{blue}{ 54681 } $ and get the remainder

$$ 74569 : 54681 = 1 \text{ ( remainder is } \color{blue}{ 19888 } \text{ ) } $$

The remainder is still positive ($ 19888 > 0 $), so we will continue with division.

Step 3 :
Divide $ 54681 $ by $ \color{blue}{ 19888 } $ and get the remainder

$$ 54681 : 19888 = 2 \text{ ( remainder is } \color{blue}{ 14905 } \text{ ) } $$

The remainder is still positive ($ 14905 > 0 $), so we will continue with division.

Step 4 :
Divide $ 19888 $ by $ \color{blue}{ 14905 } $ and get the remainder

$$ 19888 : 14905 = 1 \text{ ( remainder is } \color{blue}{ 4983 } \text{ ) } $$

The remainder is still positive ($ 4983 > 0 $), so we will continue with division.

Step 5 :
Divide $ 14905 $ by $ \color{blue}{ 4983 } $ and get the remainder

$$ 14905 : 4983 = 2 \text{ ( remainder is } \color{blue}{ 4939 } \text{ ) } $$

The remainder is still positive ($ 4939 > 0 $), so we will continue with division.

Step 6 :
Divide $ 4983 $ by $ \color{blue}{ 4939 } $ and get the remainder

$$ 4983 : 4939 = 1 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

The remainder is still positive ($ 44 > 0 $), so we will continue with division.

Step 7 :
Divide $ 4939 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 4939 : 44 = 112 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

The remainder is still positive ($ 11 > 0 $), so we will continue with division.

Step 8 :
Divide $ 44 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 44 : \color{blue}{ \boxed { 11 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.

This solution can be visualized using a Venn diagram.

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

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