Step 1 :
Divide $ 6828 $ by $ 709 $ and get the remainder

$$ 6828 : 709 = 9 \text{ ( remainder is } \color{blue}{ 447 } \text{ ) } $$

The remainder is positive ($ 447 > 0 $), so we will continue with division.

Step 2 :
Divide $ 709 $ by $ \color{blue}{ 447 } $ and get the remainder

$$ 709 : 447 = 1 \text{ ( remainder is } \color{blue}{ 262 } \text{ ) } $$

The remainder is still positive ($ 262 > 0 $), so we will continue with division.

Step 3 :
Divide $ 447 $ by $ \color{blue}{ 262 } $ and get the remainder

$$ 447 : 262 = 1 \text{ ( remainder is } \color{blue}{ 185 } \text{ ) } $$

The remainder is still positive ($ 185 > 0 $), so we will continue with division.

Step 4 :
Divide $ 262 $ by $ \color{blue}{ 185 } $ and get the remainder

$$ 262 : 185 = 1 \text{ ( remainder is } \color{blue}{ 77 } \text{ ) } $$

The remainder is still positive ($ 77 > 0 $), so we will continue with division.

Step 5 :
Divide $ 185 $ by $ \color{blue}{ 77 } $ and get the remainder

$$ 185 : 77 = 2 \text{ ( remainder is } \color{blue}{ 31 } \text{ ) } $$

The remainder is still positive ($ 31 > 0 $), so we will continue with division.

Step 6 :
Divide $ 77 $ by $ \color{blue}{ 31 } $ and get the remainder

$$ 77 : 31 = 2 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

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

Step 7 :
Divide $ 31 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 31 : 15 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 8 :
Divide $ 15 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 15 : \color{blue}{ \boxed { 1 }} = 15 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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