Step 1 :
Divide $ 3921 $ by $ 460 $ and get the remainder

$$ 3921 : 460 = 8 \text{ ( remainder is } \color{blue}{ 241 } \text{ ) } $$

The remainder is positive ($ 241 > 0 $), so we will continue with division.

Step 2 :
Divide $ 460 $ by $ \color{blue}{ 241 } $ and get the remainder

$$ 460 : 241 = 1 \text{ ( remainder is } \color{blue}{ 219 } \text{ ) } $$

The remainder is still positive ($ 219 > 0 $), so we will continue with division.

Step 3 :
Divide $ 241 $ by $ \color{blue}{ 219 } $ and get the remainder

$$ 241 : 219 = 1 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 4 :
Divide $ 219 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 219 : 22 = 9 \text{ ( remainder is } \color{blue}{ 21 } \text{ ) } $$

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

Step 5 :
Divide $ 22 $ by $ \color{blue}{ 21 } $ and get the remainder

$$ 22 : 21 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 21 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 21 : \color{blue}{ \boxed { 1 }} = 21 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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.

GCD Calculator