Step 1 :
Divide $ 16170 $ by $ 11170 $ and get the remainder

$$ 16170 : 11170 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11170 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11170 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1170 } \text{ ) } $$

The remainder is still positive ($ 1170 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1170 } $ and get the remainder

$$ 5000 : 1170 = 4 \text{ ( remainder is } \color{blue}{ 320 } \text{ ) } $$

The remainder is still positive ($ 320 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1170 $ by $ \color{blue}{ 320 } $ and get the remainder

$$ 1170 : 320 = 3 \text{ ( remainder is } \color{blue}{ 210 } \text{ ) } $$

The remainder is still positive ($ 210 > 0 $), so we will continue with division.

Step 5 :
Divide $ 320 $ by $ \color{blue}{ 210 } $ and get the remainder

$$ 320 : 210 = 1 \text{ ( remainder is } \color{blue}{ 110 } \text{ ) } $$

The remainder is still positive ($ 110 > 0 $), so we will continue with division.

Step 6 :
Divide $ 210 $ by $ \color{blue}{ 110 } $ and get the remainder

$$ 210 : 110 = 1 \text{ ( remainder is } \color{blue}{ 100 } \text{ ) } $$

The remainder is still positive ($ 100 > 0 $), so we will continue with division.

Step 7 :
Divide $ 110 $ by $ \color{blue}{ 100 } $ and get the remainder

$$ 110 : 100 = 1 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 8 :
Divide $ 100 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 100 : \color{blue}{ \boxed { 10 }} = 10 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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