Step 1 :
Divide $ 54585 $ by $ 4920 $ and get the remainder

$$ 54585 : 4920 = 11 \text{ ( remainder is } \color{blue}{ 465 } \text{ ) } $$

The remainder is positive ($ 465 > 0 $), so we will continue with division.

Step 2 :
Divide $ 4920 $ by $ \color{blue}{ 465 } $ and get the remainder

$$ 4920 : 465 = 10 \text{ ( remainder is } \color{blue}{ 270 } \text{ ) } $$

The remainder is still positive ($ 270 > 0 $), so we will continue with division.

Step 3 :
Divide $ 465 $ by $ \color{blue}{ 270 } $ and get the remainder

$$ 465 : 270 = 1 \text{ ( remainder is } \color{blue}{ 195 } \text{ ) } $$

The remainder is still positive ($ 195 > 0 $), so we will continue with division.

Step 4 :
Divide $ 270 $ by $ \color{blue}{ 195 } $ and get the remainder

$$ 270 : 195 = 1 \text{ ( remainder is } \color{blue}{ 75 } \text{ ) } $$

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

Step 5 :
Divide $ 195 $ by $ \color{blue}{ 75 } $ and get the remainder

$$ 195 : 75 = 2 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is still positive ($ 45 > 0 $), so we will continue with division.

Step 6 :
Divide $ 75 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 75 : 45 = 1 \text{ ( remainder is } \color{blue}{ 30 } \text{ ) } $$

The remainder is still positive ($ 30 > 0 $), so we will continue with division.

Step 7 :
Divide $ 45 $ by $ \color{blue}{ 30 } $ and get the remainder

$$ 45 : 30 = 1 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

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

Step 8 :
Divide $ 30 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 30 : \color{blue}{ \boxed { 15 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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