Step 1 :
Divide $ 2079 $ by $ 825 $ and get the remainder

$$ 2079 : 825 = 2 \text{ ( remainder is } \color{blue}{ 429 } \text{ ) } $$

The remainder is positive ($ 429 > 0 $), so we will continue with division.

Step 2 :
Divide $ 825 $ by $ \color{blue}{ 429 } $ and get the remainder

$$ 825 : 429 = 1 \text{ ( remainder is } \color{blue}{ 396 } \text{ ) } $$

The remainder is still positive ($ 396 > 0 $), so we will continue with division.

Step 3 :
Divide $ 429 $ by $ \color{blue}{ 396 } $ and get the remainder

$$ 429 : 396 = 1 \text{ ( remainder is } \color{blue}{ 33 } \text{ ) } $$

The remainder is still positive ($ 33 > 0 $), so we will continue with division.

Step 4 :
Divide $ 396 $ by $ \color{blue}{ 33 } $ and get the remainder

$$ 396 : \color{blue}{ \boxed { 33 }} = 12 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 33 }} $.

This solution can be visualized using a Venn diagram.

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

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