Step 1 :
Divide $ 16270 $ by $ 11270 $ and get the remainder

$$ 16270 : 11270 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11270 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11270 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1270 } \text{ ) } $$

The remainder is still positive ($ 1270 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1270 } $ and get the remainder

$$ 5000 : 1270 = 3 \text{ ( remainder is } \color{blue}{ 1190 } \text{ ) } $$

The remainder is still positive ($ 1190 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1270 $ by $ \color{blue}{ 1190 } $ and get the remainder

$$ 1270 : 1190 = 1 \text{ ( remainder is } \color{blue}{ 80 } \text{ ) } $$

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

Step 5 :
Divide $ 1190 $ by $ \color{blue}{ 80 } $ and get the remainder

$$ 1190 : 80 = 14 \text{ ( remainder is } \color{blue}{ 70 } \text{ ) } $$

The remainder is still positive ($ 70 > 0 $), so we will continue with division.

Step 6 :
Divide $ 80 $ by $ \color{blue}{ 70 } $ and get the remainder

$$ 80 : 70 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 7 :
Divide $ 70 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 70 : \color{blue}{ \boxed { 10 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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