Step 1 :
Divide $ 4288 $ by $ 464 $ and get the remainder

$$ 4288 : 464 = 9 \text{ ( remainder is } \color{blue}{ 112 } \text{ ) } $$

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

Step 2 :
Divide $ 464 $ by $ \color{blue}{ 112 } $ and get the remainder

$$ 464 : 112 = 4 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 3 :
Divide $ 112 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 112 : \color{blue}{ \boxed { 16 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 16 }} $.

This solution can be visualized using a Venn diagram.

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

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