Step 1 :
Divide $ 153 $ by $ 114 $ and get the remainder

$$ 153 : 114 = 1 \text{ ( remainder is } \color{blue}{ 39 } \text{ ) } $$

The remainder is positive ($ 39 > 0 $), so we will continue with division.

Step 2 :
Divide $ 114 $ by $ \color{blue}{ 39 } $ and get the remainder

$$ 114 : 39 = 2 \text{ ( remainder is } \color{blue}{ 36 } \text{ ) } $$

The remainder is still positive ($ 36 > 0 $), so we will continue with division.

Step 3 :
Divide $ 39 $ by $ \color{blue}{ 36 } $ and get the remainder

$$ 39 : 36 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 4 :
Divide $ 36 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 36 : \color{blue}{ \boxed { 3 }} = 12 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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