Step 1 :
Divide $ 350 $ by $ 45 $ and get the remainder

$$ 350 : 45 = 7 \text{ ( remainder is } \color{blue}{ 35 } \text{ ) } $$

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

Step 2 :
Divide $ 45 $ by $ \color{blue}{ 35 } $ and get the remainder

$$ 45 : 35 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 3 :
Divide $ 35 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 35 : 10 = 3 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

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

Step 4 :
Divide $ 10 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 10 : \color{blue}{ \boxed { 5 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 5 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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