Step 1 :
Divide $ 7268 $ by $ 1518 $ and get the remainder

$$ 7268 : 1518 = 4 \text{ ( remainder is } \color{blue}{ 1196 } \text{ ) } $$

The remainder is positive ($ 1196 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1518 $ by $ \color{blue}{ 1196 } $ and get the remainder

$$ 1518 : 1196 = 1 \text{ ( remainder is } \color{blue}{ 322 } \text{ ) } $$

The remainder is still positive ($ 322 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1196 $ by $ \color{blue}{ 322 } $ and get the remainder

$$ 1196 : 322 = 3 \text{ ( remainder is } \color{blue}{ 230 } \text{ ) } $$

The remainder is still positive ($ 230 > 0 $), so we will continue with division.

Step 4 :
Divide $ 322 $ by $ \color{blue}{ 230 } $ and get the remainder

$$ 322 : 230 = 1 \text{ ( remainder is } \color{blue}{ 92 } \text{ ) } $$

The remainder is still positive ($ 92 > 0 $), so we will continue with division.

Step 5 :
Divide $ 230 $ by $ \color{blue}{ 92 } $ and get the remainder

$$ 230 : 92 = 2 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 6 :
Divide $ 92 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 92 : \color{blue}{ \boxed { 46 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 46 }} $.

This solution can be visualized using a Venn diagram.

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

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