Step 1 :
Divide $ 10642 $ by $ 3006 $ and get the remainder

$$ 10642 : 3006 = 3 \text{ ( remainder is } \color{blue}{ 1624 } \text{ ) } $$

The remainder is positive ($ 1624 > 0 $), so we will continue with division.

Step 2 :
Divide $ 3006 $ by $ \color{blue}{ 1624 } $ and get the remainder

$$ 3006 : 1624 = 1 \text{ ( remainder is } \color{blue}{ 1382 } \text{ ) } $$

The remainder is still positive ($ 1382 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1624 $ by $ \color{blue}{ 1382 } $ and get the remainder

$$ 1624 : 1382 = 1 \text{ ( remainder is } \color{blue}{ 242 } \text{ ) } $$

The remainder is still positive ($ 242 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1382 $ by $ \color{blue}{ 242 } $ and get the remainder

$$ 1382 : 242 = 5 \text{ ( remainder is } \color{blue}{ 172 } \text{ ) } $$

The remainder is still positive ($ 172 > 0 $), so we will continue with division.

Step 5 :
Divide $ 242 $ by $ \color{blue}{ 172 } $ and get the remainder

$$ 242 : 172 = 1 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 6 :
Divide $ 172 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 172 : 70 = 2 \text{ ( remainder is } \color{blue}{ 32 } \text{ ) } $$

The remainder is still positive ($ 32 > 0 $), so we will continue with division.

Step 7 :
Divide $ 70 $ by $ \color{blue}{ 32 } $ and get the remainder

$$ 70 : 32 = 2 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 8 :
Divide $ 32 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 32 : 6 = 5 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 9 :
Divide $ 6 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 6 : \color{blue}{ \boxed { 2 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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