Step 1 :
Divide $ 5445 $ by $ 2550 $ and get the remainder

$$ 5445 : 2550 = 2 \text{ ( remainder is } \color{blue}{ 345 } \text{ ) } $$

The remainder is positive ($ 345 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2550 $ by $ \color{blue}{ 345 } $ and get the remainder

$$ 2550 : 345 = 7 \text{ ( remainder is } \color{blue}{ 135 } \text{ ) } $$

The remainder is still positive ($ 135 > 0 $), so we will continue with division.

Step 3 :
Divide $ 345 $ by $ \color{blue}{ 135 } $ and get the remainder

$$ 345 : 135 = 2 \text{ ( remainder is } \color{blue}{ 75 } \text{ ) } $$

The remainder is still positive ($ 75 > 0 $), so we will continue with division.

Step 4 :
Divide $ 135 $ by $ \color{blue}{ 75 } $ and get the remainder

$$ 135 : 75 = 1 \text{ ( remainder is } \color{blue}{ 60 } \text{ ) } $$

The remainder is still positive ($ 60 > 0 $), so we will continue with division.

Step 5 :
Divide $ 75 $ by $ \color{blue}{ 60 } $ and get the remainder

$$ 75 : 60 = 1 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 6 :
Divide $ 60 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 60 : \color{blue}{ \boxed { 15 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 15 }} $.

This solution can be visualized using a Venn diagram.

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

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