Step 1 :
Divide $ 52650 $ by $ 36900 $ and get the remainder

$$ 52650 : 36900 = 1 \text{ ( remainder is } \color{blue}{ 15750 } \text{ ) } $$

The remainder is positive ($ 15750 > 0 $), so we will continue with division.

Step 2 :
Divide $ 36900 $ by $ \color{blue}{ 15750 } $ and get the remainder

$$ 36900 : 15750 = 2 \text{ ( remainder is } \color{blue}{ 5400 } \text{ ) } $$

The remainder is still positive ($ 5400 > 0 $), so we will continue with division.

Step 3 :
Divide $ 15750 $ by $ \color{blue}{ 5400 } $ and get the remainder

$$ 15750 : 5400 = 2 \text{ ( remainder is } \color{blue}{ 4950 } \text{ ) } $$

The remainder is still positive ($ 4950 > 0 $), so we will continue with division.

Step 4 :
Divide $ 5400 $ by $ \color{blue}{ 4950 } $ and get the remainder

$$ 5400 : 4950 = 1 \text{ ( remainder is } \color{blue}{ 450 } \text{ ) } $$

The remainder is still positive ($ 450 > 0 $), so we will continue with division.

Step 5 :
Divide $ 4950 $ by $ \color{blue}{ 450 } $ and get the remainder

$$ 4950 : \color{blue}{ \boxed { 450 }} = 11 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 450 }} $.

This solution can be visualized using a Venn diagram.

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

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