Step 1 :
Divide $ 813 $ by $ 708 $ and get the remainder

$$ 813 : 708 = 1 \text{ ( remainder is } \color{blue}{ 105 } \text{ ) } $$

The remainder is positive ($ 105 > 0 $), so we will continue with division.

Step 2 :
Divide $ 708 $ by $ \color{blue}{ 105 } $ and get the remainder

$$ 708 : 105 = 6 \text{ ( remainder is } \color{blue}{ 78 } \text{ ) } $$

The remainder is still positive ($ 78 > 0 $), so we will continue with division.

Step 3 :
Divide $ 105 $ by $ \color{blue}{ 78 } $ and get the remainder

$$ 105 : 78 = 1 \text{ ( remainder is } \color{blue}{ 27 } \text{ ) } $$

The remainder is still positive ($ 27 > 0 $), so we will continue with division.

Step 4 :
Divide $ 78 $ by $ \color{blue}{ 27 } $ and get the remainder

$$ 78 : 27 = 2 \text{ ( remainder is } \color{blue}{ 24 } \text{ ) } $$

The remainder is still positive ($ 24 > 0 $), so we will continue with division.

Step 5 :
Divide $ 27 $ by $ \color{blue}{ 24 } $ and get the remainder

$$ 27 : 24 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 6 :
Divide $ 24 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 24 : \color{blue}{ \boxed { 3 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

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