Step 1 :
Divide $ 5784 $ by $ 280 $ and get the remainder

$$ 5784 : 280 = 20 \text{ ( remainder is } \color{blue}{ 184 } \text{ ) } $$

The remainder is positive ($ 184 > 0 $), so we will continue with division.

Step 2 :
Divide $ 280 $ by $ \color{blue}{ 184 } $ and get the remainder

$$ 280 : 184 = 1 \text{ ( remainder is } \color{blue}{ 96 } \text{ ) } $$

The remainder is still positive ($ 96 > 0 $), so we will continue with division.

Step 3 :
Divide $ 184 $ by $ \color{blue}{ 96 } $ and get the remainder

$$ 184 : 96 = 1 \text{ ( remainder is } \color{blue}{ 88 } \text{ ) } $$

The remainder is still positive ($ 88 > 0 $), so we will continue with division.

Step 4 :
Divide $ 96 $ by $ \color{blue}{ 88 } $ and get the remainder

$$ 96 : 88 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 5 :
Divide $ 88 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 88 : \color{blue}{ \boxed { 8 }} = 11 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator