Step 1 :
Divide $ 43336 $ by $ 332 $ and get the remainder

$$ 43336 : 332 = 130 \text{ ( remainder is } \color{blue}{ 176 } \text{ ) } $$

The remainder is positive ($ 176 > 0 $), so we will continue with division.

Step 2 :
Divide $ 332 $ by $ \color{blue}{ 176 } $ and get the remainder

$$ 332 : 176 = 1 \text{ ( remainder is } \color{blue}{ 156 } \text{ ) } $$

The remainder is still positive ($ 156 > 0 $), so we will continue with division.

Step 3 :
Divide $ 176 $ by $ \color{blue}{ 156 } $ and get the remainder

$$ 176 : 156 = 1 \text{ ( remainder is } \color{blue}{ 20 } \text{ ) } $$

The remainder is still positive ($ 20 > 0 $), so we will continue with division.

Step 4 :
Divide $ 156 $ by $ \color{blue}{ 20 } $ and get the remainder

$$ 156 : 20 = 7 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

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

Step 5 :
Divide $ 20 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 20 : 16 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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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