Step 1 :
Divide $ 4121 $ by $ 460 $ and get the remainder

$$ 4121 : 460 = 8 \text{ ( remainder is } \color{blue}{ 441 } \text{ ) } $$

The remainder is positive ($ 441 > 0 $), so we will continue with division.

Step 2 :
Divide $ 460 $ by $ \color{blue}{ 441 } $ and get the remainder

$$ 460 : 441 = 1 \text{ ( remainder is } \color{blue}{ 19 } \text{ ) } $$

The remainder is still positive ($ 19 > 0 $), so we will continue with division.

Step 3 :
Divide $ 441 $ by $ \color{blue}{ 19 } $ and get the remainder

$$ 441 : 19 = 23 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 4 :
Divide $ 19 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 19 : 4 = 4 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 5 :
Divide $ 4 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 4 : 3 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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