Step 1 :
Divide $ 4536 $ by $ 1372 $ and get the remainder

$$ 4536 : 1372 = 3 \text{ ( remainder is } \color{blue}{ 420 } \text{ ) } $$

The remainder is positive ($ 420 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1372 $ by $ \color{blue}{ 420 } $ and get the remainder

$$ 1372 : 420 = 3 \text{ ( remainder is } \color{blue}{ 112 } \text{ ) } $$

The remainder is still positive ($ 112 > 0 $), so we will continue with division.

Step 3 :
Divide $ 420 $ by $ \color{blue}{ 112 } $ and get the remainder

$$ 420 : 112 = 3 \text{ ( remainder is } \color{blue}{ 84 } \text{ ) } $$

The remainder is still positive ($ 84 > 0 $), so we will continue with division.

Step 4 :
Divide $ 112 $ by $ \color{blue}{ 84 } $ and get the remainder

$$ 112 : 84 = 1 \text{ ( remainder is } \color{blue}{ 28 } \text{ ) } $$

The remainder is still positive ($ 28 > 0 $), so we will continue with division.

Step 5 :
Divide $ 84 $ by $ \color{blue}{ 28 } $ and get the remainder

$$ 84 : \color{blue}{ \boxed { 28 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 28 }} $.

This solution can be visualized using a Venn diagram.

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

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