Step 1 :
Divide $ 6828 $ by $ 651 $ and get the remainder

$$ 6828 : 651 = 10 \text{ ( remainder is } \color{blue}{ 318 } \text{ ) } $$

The remainder is positive ($ 318 > 0 $), so we will continue with division.

Step 2 :
Divide $ 651 $ by $ \color{blue}{ 318 } $ and get the remainder

$$ 651 : 318 = 2 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 3 :
Divide $ 318 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 318 : 15 = 21 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 4 :
Divide $ 15 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 15 : \color{blue}{ \boxed { 3 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator