Step 1 :
Divide $ 3572 $ by $ 288 $ and get the remainder

$$ 3572 : 288 = 12 \text{ ( remainder is } \color{blue}{ 116 } \text{ ) } $$

The remainder is positive ($ 116 > 0 $), so we will continue with division.

Step 2 :
Divide $ 288 $ by $ \color{blue}{ 116 } $ and get the remainder

$$ 288 : 116 = 2 \text{ ( remainder is } \color{blue}{ 56 } \text{ ) } $$

The remainder is still positive ($ 56 > 0 $), so we will continue with division.

Step 3 :
Divide $ 116 $ by $ \color{blue}{ 56 } $ and get the remainder

$$ 116 : 56 = 2 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 4 :
Divide $ 56 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 56 : \color{blue}{ \boxed { 4 }} = 14 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.

This solution can be visualized using a Venn diagram.

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

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