Step 1 :
Divide $ 31256 $ by $ 4788 $ and get the remainder

$$ 31256 : 4788 = 6 \text{ ( remainder is } \color{blue}{ 2528 } \text{ ) } $$

The remainder is positive ($ 2528 > 0 $), so we will continue with division.

Step 2 :
Divide $ 4788 $ by $ \color{blue}{ 2528 } $ and get the remainder

$$ 4788 : 2528 = 1 \text{ ( remainder is } \color{blue}{ 2260 } \text{ ) } $$

The remainder is still positive ($ 2260 > 0 $), so we will continue with division.

Step 3 :
Divide $ 2528 $ by $ \color{blue}{ 2260 } $ and get the remainder

$$ 2528 : 2260 = 1 \text{ ( remainder is } \color{blue}{ 268 } \text{ ) } $$

The remainder is still positive ($ 268 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2260 $ by $ \color{blue}{ 268 } $ and get the remainder

$$ 2260 : 268 = 8 \text{ ( remainder is } \color{blue}{ 116 } \text{ ) } $$

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

Step 5 :
Divide $ 268 $ by $ \color{blue}{ 116 } $ and get the remainder

$$ 268 : 116 = 2 \text{ ( remainder is } \color{blue}{ 36 } \text{ ) } $$

The remainder is still positive ($ 36 > 0 $), so we will continue with division.

Step 6 :
Divide $ 116 $ by $ \color{blue}{ 36 } $ and get the remainder

$$ 116 : 36 = 3 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

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

Step 7 :
Divide $ 36 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 36 : 8 = 4 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 8 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 8 : \color{blue}{ \boxed { 4 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

GCD Calculator