Step 1 :
Divide $ 1071 $ by $ 482 $ and get the remainder

$$ 1071 : 482 = 2 \text{ ( remainder is } \color{blue}{ 107 } \text{ ) } $$

The remainder is positive ($ 107 > 0 $), so we will continue with division.

Step 2 :
Divide $ 482 $ by $ \color{blue}{ 107 } $ and get the remainder

$$ 482 : 107 = 4 \text{ ( remainder is } \color{blue}{ 54 } \text{ ) } $$

The remainder is still positive ($ 54 > 0 $), so we will continue with division.

Step 3 :
Divide $ 107 $ by $ \color{blue}{ 54 } $ and get the remainder

$$ 107 : 54 = 1 \text{ ( remainder is } \color{blue}{ 53 } \text{ ) } $$

The remainder is still positive ($ 53 > 0 $), so we will continue with division.

Step 4 :
Divide $ 54 $ by $ \color{blue}{ 53 } $ and get the remainder

$$ 54 : 53 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 5 :
Divide $ 53 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 53 : \color{blue}{ \boxed { 1 }} = 53 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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