Step 1 :
Divide $ 233 $ by $ 144 $ and get the remainder

$$ 233 : 144 = 1 \text{ ( remainder is } \color{blue}{ 89 } \text{ ) } $$

The remainder is positive ($ 89 > 0 $), so we will continue with division.

Step 2 :
Divide $ 144 $ by $ \color{blue}{ 89 } $ and get the remainder

$$ 144 : 89 = 1 \text{ ( remainder is } \color{blue}{ 55 } \text{ ) } $$

The remainder is still positive ($ 55 > 0 $), so we will continue with division.

Step 3 :
Divide $ 89 $ by $ \color{blue}{ 55 } $ and get the remainder

$$ 89 : 55 = 1 \text{ ( remainder is } \color{blue}{ 34 } \text{ ) } $$

The remainder is still positive ($ 34 > 0 $), so we will continue with division.

Step 4 :
Divide $ 55 $ by $ \color{blue}{ 34 } $ and get the remainder

$$ 55 : 34 = 1 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

The remainder is still positive ($ 21 > 0 $), so we will continue with division.

Step 5 :
Divide $ 34 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 34 : 21 = 1 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 6 :
Divide $ 21 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 21 : 13 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 7 :
Divide $ 13 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 13 : 8 = 1 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

The remainder is still positive ($ 5 > 0 $), so we will continue with division.

Step 8 :
Divide $ 8 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 8 : 5 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 9 :
Divide $ 5 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 5 : 3 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 10 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 11 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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