Step 1 :
Divide $ 8974 $ by $ 1518 $ and get the remainder

$$ 8974 : 1518 = 5 \text{ ( remainder is } \color{blue}{ 1384 } \text{ ) } $$

The remainder is positive ($ 1384 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1518 $ by $ \color{blue}{ 1384 } $ and get the remainder

$$ 1518 : 1384 = 1 \text{ ( remainder is } \color{blue}{ 134 } \text{ ) } $$

The remainder is still positive ($ 134 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1384 $ by $ \color{blue}{ 134 } $ and get the remainder

$$ 1384 : 134 = 10 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

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

Step 4 :
Divide $ 134 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 134 : 44 = 3 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 5 :
Divide $ 44 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 44 : \color{blue}{ \boxed { 2 }} = 22 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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