Step 1 :
Divide $ 1571 $ by $ 1233 $ and get the remainder

$$ 1571 : 1233 = 1 \text{ ( remainder is } \color{blue}{ 338 } \text{ ) } $$

The remainder is positive ($ 338 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1233 $ by $ \color{blue}{ 338 } $ and get the remainder

$$ 1233 : 338 = 3 \text{ ( remainder is } \color{blue}{ 219 } \text{ ) } $$

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

Step 3 :
Divide $ 338 $ by $ \color{blue}{ 219 } $ and get the remainder

$$ 338 : 219 = 1 \text{ ( remainder is } \color{blue}{ 119 } \text{ ) } $$

The remainder is still positive ($ 119 > 0 $), so we will continue with division.

Step 4 :
Divide $ 219 $ by $ \color{blue}{ 119 } $ and get the remainder

$$ 219 : 119 = 1 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

The remainder is still positive ($ 100 > 0 $), so we will continue with division.

Step 5 :
Divide $ 119 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 119 : 100 = 1 \text{ ( remainder is } \color{blue}{ 19 } \text{ ) } $$

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

Step 6 :
Divide $ 100 $ by $ \color{blue}{ 19 } $ and get the remainder

$$ 100 : 19 = 5 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

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

Step 7 :
Divide $ 19 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 19 : 5 = 3 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 8 :
Divide $ 5 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 5 : 4 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 9 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 1 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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