Step 1 :
Divide $ 1203 $ by $ 460 $ and get the remainder

$$ 1203 : 460 = 2 \text{ ( remainder is } \color{blue}{ 283 } \text{ ) } $$

The remainder is positive ($ 283 > 0 $), so we will continue with division.

Step 2 :
Divide $ 460 $ by $ \color{blue}{ 283 } $ and get the remainder

$$ 460 : 283 = 1 \text{ ( remainder is } \color{blue}{ 177 } \text{ ) } $$

The remainder is still positive ($ 177 > 0 $), so we will continue with division.

Step 3 :
Divide $ 283 $ by $ \color{blue}{ 177 } $ and get the remainder

$$ 283 : 177 = 1 \text{ ( remainder is } \color{blue}{ 106 } \text{ ) } $$

The remainder is still positive ($ 106 > 0 $), so we will continue with division.

Step 4 :
Divide $ 177 $ by $ \color{blue}{ 106 } $ and get the remainder

$$ 177 : 106 = 1 \text{ ( remainder is } \color{blue}{ 71 } \text{ ) } $$

The remainder is still positive ($ 71 > 0 $), so we will continue with division.

Step 5 :
Divide $ 106 $ by $ \color{blue}{ 71 } $ and get the remainder

$$ 106 : 71 = 1 \text{ ( remainder is } \color{blue}{ 35 } \text{ ) } $$

The remainder is still positive ($ 35 > 0 $), so we will continue with division.

Step 6 :
Divide $ 71 $ by $ \color{blue}{ 35 } $ and get the remainder

$$ 71 : 35 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 35 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 35 : \color{blue}{ \boxed { 1 }} = 35 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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