Step 1 :
Divide $ 8429 $ by $ 1518 $ and get the remainder

$$ 8429 : 1518 = 5 \text{ ( remainder is } \color{blue}{ 839 } \text{ ) } $$

The remainder is positive ($ 839 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1518 $ by $ \color{blue}{ 839 } $ and get the remainder

$$ 1518 : 839 = 1 \text{ ( remainder is } \color{blue}{ 679 } \text{ ) } $$

The remainder is still positive ($ 679 > 0 $), so we will continue with division.

Step 3 :
Divide $ 839 $ by $ \color{blue}{ 679 } $ and get the remainder

$$ 839 : 679 = 1 \text{ ( remainder is } \color{blue}{ 160 } \text{ ) } $$

The remainder is still positive ($ 160 > 0 $), so we will continue with division.

Step 4 :
Divide $ 679 $ by $ \color{blue}{ 160 } $ and get the remainder

$$ 679 : 160 = 4 \text{ ( remainder is } \color{blue}{ 39 } \text{ ) } $$

The remainder is still positive ($ 39 > 0 $), so we will continue with division.

Step 5 :
Divide $ 160 $ by $ \color{blue}{ 39 } $ and get the remainder

$$ 160 : 39 = 4 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 6 :
Divide $ 39 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 39 : 4 = 9 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 7 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 4 : 3 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 8 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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