Step 1 :
Divide $ 146 $ by $ 96 $ and get the remainder

$$ 146 : 96 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is positive ($ 50 > 0 $), so we will continue with division.

Step 2 :
Divide $ 96 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 96 : 50 = 1 \text{ ( remainder is } \color{blue}{ 46 } \text{ ) } $$

The remainder is still positive ($ 46 > 0 $), so we will continue with division.

Step 3 :
Divide $ 50 $ by $ \color{blue}{ 46 } $ and get the remainder

$$ 50 : 46 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 4 :
Divide $ 46 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 46 : 4 = 11 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 5 :
Divide $ 4 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 2 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.

This solution can be visualized using a Venn diagram.

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

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