Step 1 :
Divide $ 1758 $ by $ 337 $ and get the remainder

$$ 1758 : 337 = 5 \text{ ( remainder is } \color{blue}{ 73 } \text{ ) } $$

The remainder is positive ($ 73 > 0 $), so we will continue with division.

Step 2 :
Divide $ 337 $ by $ \color{blue}{ 73 } $ and get the remainder

$$ 337 : 73 = 4 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is still positive ($ 45 > 0 $), so we will continue with division.

Step 3 :
Divide $ 73 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 73 : 45 = 1 \text{ ( remainder is } \color{blue}{ 28 } \text{ ) } $$

The remainder is still positive ($ 28 > 0 $), so we will continue with division.

Step 4 :
Divide $ 45 $ by $ \color{blue}{ 28 } $ and get the remainder

$$ 45 : 28 = 1 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 5 :
Divide $ 28 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 28 : 17 = 1 \text{ ( remainder is } \color{blue}{ 11 } \text{ ) } $$

The remainder is still positive ($ 11 > 0 $), so we will continue with division.

Step 6 :
Divide $ 17 $ by $ \color{blue}{ 11 } $ and get the remainder

$$ 17 : 11 = 1 \text{ ( remainder is } \color{blue}{ 6 } \text{ ) } $$

The remainder is still positive ($ 6 > 0 $), so we will continue with division.

Step 7 :
Divide $ 11 $ by $ \color{blue}{ 6 } $ and get the remainder

$$ 11 : 6 = 1 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

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

Step 8 :
Divide $ 6 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 6 : 5 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 9 :
Divide $ 5 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 5 : \color{blue}{ \boxed { 1 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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