Step 1 :
Divide $ 144227 $ by $ 58483 $ and get the remainder

$$ 144227 : 58483 = 2 \text{ ( remainder is } \color{blue}{ 27261 } \text{ ) } $$

The remainder is positive ($ 27261 > 0 $), so we will continue with division.

Step 2 :
Divide $ 58483 $ by $ \color{blue}{ 27261 } $ and get the remainder

$$ 58483 : 27261 = 2 \text{ ( remainder is } \color{blue}{ 3961 } \text{ ) } $$

The remainder is still positive ($ 3961 > 0 $), so we will continue with division.

Step 3 :
Divide $ 27261 $ by $ \color{blue}{ 3961 } $ and get the remainder

$$ 27261 : 3961 = 6 \text{ ( remainder is } \color{blue}{ 3495 } \text{ ) } $$

The remainder is still positive ($ 3495 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3961 $ by $ \color{blue}{ 3495 } $ and get the remainder

$$ 3961 : 3495 = 1 \text{ ( remainder is } \color{blue}{ 466 } \text{ ) } $$

The remainder is still positive ($ 466 > 0 $), so we will continue with division.

Step 5 :
Divide $ 3495 $ by $ \color{blue}{ 466 } $ and get the remainder

$$ 3495 : 466 = 7 \text{ ( remainder is } \color{blue}{ 233 } \text{ ) } $$

The remainder is still positive ($ 233 > 0 $), so we will continue with division.

Step 6 :
Divide $ 466 $ by $ \color{blue}{ 233 } $ and get the remainder

$$ 466 : \color{blue}{ \boxed { 233 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 233 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator