Step 1 :
Divide $ 8428 $ by $ 1518 $ and get the remainder

$$ 8428 : 1518 = 5 \text{ ( remainder is } \color{blue}{ 838 } \text{ ) } $$

The remainder is positive ($ 838 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1518 $ by $ \color{blue}{ 838 } $ and get the remainder

$$ 1518 : 838 = 1 \text{ ( remainder is } \color{blue}{ 680 } \text{ ) } $$

The remainder is still positive ($ 680 > 0 $), so we will continue with division.

Step 3 :
Divide $ 838 $ by $ \color{blue}{ 680 } $ and get the remainder

$$ 838 : 680 = 1 \text{ ( remainder is } \color{blue}{ 158 } \text{ ) } $$

The remainder is still positive ($ 158 > 0 $), so we will continue with division.

Step 4 :
Divide $ 680 $ by $ \color{blue}{ 158 } $ and get the remainder

$$ 680 : 158 = 4 \text{ ( remainder is } \color{blue}{ 48 } \text{ ) } $$

The remainder is still positive ($ 48 > 0 $), so we will continue with division.

Step 5 :
Divide $ 158 $ by $ \color{blue}{ 48 } $ and get the remainder

$$ 158 : 48 = 3 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 6 :
Divide $ 48 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 48 : 14 = 3 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

Step 7 :
Divide $ 14 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 14 : 6 = 2 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 8 :
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.

GCD Calculator