Step 1 :
Divide $ 18450 $ by $ 13450 $ and get the remainder

$$ 18450 : 13450 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

The remainder is positive ($ 5000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 13450 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13450 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3450 } \text{ ) } $$

The remainder is still positive ($ 3450 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3450 } $ and get the remainder

$$ 5000 : 3450 = 1 \text{ ( remainder is } \color{blue}{ 1550 } \text{ ) } $$

The remainder is still positive ($ 1550 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3450 $ by $ \color{blue}{ 1550 } $ and get the remainder

$$ 3450 : 1550 = 2 \text{ ( remainder is } \color{blue}{ 350 } \text{ ) } $$

The remainder is still positive ($ 350 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1550 $ by $ \color{blue}{ 350 } $ and get the remainder

$$ 1550 : 350 = 4 \text{ ( remainder is } \color{blue}{ 150 } \text{ ) } $$

The remainder is still positive ($ 150 > 0 $), so we will continue with division.

Step 6 :
Divide $ 350 $ by $ \color{blue}{ 150 } $ and get the remainder

$$ 350 : 150 = 2 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is still positive ($ 50 > 0 $), so we will continue with division.

Step 7 :
Divide $ 150 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 150 : \color{blue}{ \boxed { 50 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 50 }} $.

This solution can be visualized using a Venn diagram.

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

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