Step 1 :
Divide $ 7266 $ by $ 1518 $ and get the remainder

$$ 7266 : 1518 = 4 \text{ ( remainder is } \color{blue}{ 1194 } \text{ ) } $$

The remainder is positive ($ 1194 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1518 $ by $ \color{blue}{ 1194 } $ and get the remainder

$$ 1518 : 1194 = 1 \text{ ( remainder is } \color{blue}{ 324 } \text{ ) } $$

The remainder is still positive ($ 324 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1194 $ by $ \color{blue}{ 324 } $ and get the remainder

$$ 1194 : 324 = 3 \text{ ( remainder is } \color{blue}{ 222 } \text{ ) } $$

The remainder is still positive ($ 222 > 0 $), so we will continue with division.

Step 4 :
Divide $ 324 $ by $ \color{blue}{ 222 } $ and get the remainder

$$ 324 : 222 = 1 \text{ ( remainder is } \color{blue}{ 102 } \text{ ) } $$

The remainder is still positive ($ 102 > 0 $), so we will continue with division.

Step 5 :
Divide $ 222 $ by $ \color{blue}{ 102 } $ and get the remainder

$$ 222 : 102 = 2 \text{ ( remainder is } \color{blue}{ 18 } \text{ ) } $$

The remainder is still positive ($ 18 > 0 $), so we will continue with division.

Step 6 :
Divide $ 102 $ by $ \color{blue}{ 18 } $ and get the remainder

$$ 102 : 18 = 5 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 7 :
Divide $ 18 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 18 : 12 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

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

Step 8 :
Divide $ 12 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 12 : \color{blue}{ \boxed { 6 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator