Step 1 :
Divide $ 4801 $ by $ 500 $ and get the remainder

$$ 4801 : 500 = 9 \text{ ( remainder is } \color{blue}{ 301 } \text{ ) } $$

The remainder is positive ($ 301 > 0 $), so we will continue with division.

Step 2 :
Divide $ 500 $ by $ \color{blue}{ 301 } $ and get the remainder

$$ 500 : 301 = 1 \text{ ( remainder is } \color{blue}{ 199 } \text{ ) } $$

The remainder is still positive ($ 199 > 0 $), so we will continue with division.

Step 3 :
Divide $ 301 $ by $ \color{blue}{ 199 } $ and get the remainder

$$ 301 : 199 = 1 \text{ ( remainder is } \color{blue}{ 102 } \text{ ) } $$

The remainder is still positive ($ 102 > 0 $), so we will continue with division.

Step 4 :
Divide $ 199 $ by $ \color{blue}{ 102 } $ and get the remainder

$$ 199 : 102 = 1 \text{ ( remainder is } \color{blue}{ 97 } \text{ ) } $$

The remainder is still positive ($ 97 > 0 $), so we will continue with division.

Step 5 :
Divide $ 102 $ by $ \color{blue}{ 97 } $ and get the remainder

$$ 102 : 97 = 1 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

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

Step 6 :
Divide $ 97 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 97 : 5 = 19 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

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

Step 7 :
Divide $ 5 $ by $ \color{blue}{ 2 } $ and get the remainder

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

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

Step 8 :
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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