Step 1 :
Divide $ 18070 $ by $ 13070 $ and get the remainder

$$ 18070 : 13070 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 13070 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 13070 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 3070 } \text{ ) } $$

The remainder is still positive ($ 3070 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 3070 } $ and get the remainder

$$ 5000 : 3070 = 1 \text{ ( remainder is } \color{blue}{ 1930 } \text{ ) } $$

The remainder is still positive ($ 1930 > 0 $), so we will continue with division.

Step 4 :
Divide $ 3070 $ by $ \color{blue}{ 1930 } $ and get the remainder

$$ 3070 : 1930 = 1 \text{ ( remainder is } \color{blue}{ 1140 } \text{ ) } $$

The remainder is still positive ($ 1140 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1930 $ by $ \color{blue}{ 1140 } $ and get the remainder

$$ 1930 : 1140 = 1 \text{ ( remainder is } \color{blue}{ 790 } \text{ ) } $$

The remainder is still positive ($ 790 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1140 $ by $ \color{blue}{ 790 } $ and get the remainder

$$ 1140 : 790 = 1 \text{ ( remainder is } \color{blue}{ 350 } \text{ ) } $$

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

Step 7 :
Divide $ 790 $ by $ \color{blue}{ 350 } $ and get the remainder

$$ 790 : 350 = 2 \text{ ( remainder is } \color{blue}{ 90 } \text{ ) } $$

The remainder is still positive ($ 90 > 0 $), so we will continue with division.

Step 8 :
Divide $ 350 $ by $ \color{blue}{ 90 } $ and get the remainder

$$ 350 : 90 = 3 \text{ ( remainder is } \color{blue}{ 80 } \text{ ) } $$

The remainder is still positive ($ 80 > 0 $), so we will continue with division.

Step 9 :
Divide $ 90 $ by $ \color{blue}{ 80 } $ and get the remainder

$$ 90 : 80 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 10 :
Divide $ 80 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 80 : \color{blue}{ \boxed { 10 }} = 8 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

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

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