Step 1 :
Divide $ 2332 $ by $ 828 $ and get the remainder

$$ 2332 : 828 = 2 \text{ ( remainder is } \color{blue}{ 676 } \text{ ) } $$

The remainder is positive ($ 676 > 0 $), so we will continue with division.

Step 2 :
Divide $ 828 $ by $ \color{blue}{ 676 } $ and get the remainder

$$ 828 : 676 = 1 \text{ ( remainder is } \color{blue}{ 152 } \text{ ) } $$

The remainder is still positive ($ 152 > 0 $), so we will continue with division.

Step 3 :
Divide $ 676 $ by $ \color{blue}{ 152 } $ and get the remainder

$$ 676 : 152 = 4 \text{ ( remainder is } \color{blue}{ 68 } \text{ ) } $$

The remainder is still positive ($ 68 > 0 $), so we will continue with division.

Step 4 :
Divide $ 152 $ by $ \color{blue}{ 68 } $ and get the remainder

$$ 152 : 68 = 2 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 5 :
Divide $ 68 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 68 : 16 = 4 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 6 :
Divide $ 16 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 16 : \color{blue}{ \boxed { 4 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

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