Step 1 :
Divide $ 11155 $ by $ 6897 $ and get the remainder

$$ 11155 : 6897 = 1 \text{ ( remainder is } \color{blue}{ 4258 } \text{ ) } $$

The remainder is positive ($ 4258 > 0 $), so we will continue with division.

Step 2 :
Divide $ 6897 $ by $ \color{blue}{ 4258 } $ and get the remainder

$$ 6897 : 4258 = 1 \text{ ( remainder is } \color{blue}{ 2639 } \text{ ) } $$

The remainder is still positive ($ 2639 > 0 $), so we will continue with division.

Step 3 :
Divide $ 4258 $ by $ \color{blue}{ 2639 } $ and get the remainder

$$ 4258 : 2639 = 1 \text{ ( remainder is } \color{blue}{ 1619 } \text{ ) } $$

The remainder is still positive ($ 1619 > 0 $), so we will continue with division.

Step 4 :
Divide $ 2639 $ by $ \color{blue}{ 1619 } $ and get the remainder

$$ 2639 : 1619 = 1 \text{ ( remainder is } \color{blue}{ 1020 } \text{ ) } $$

The remainder is still positive ($ 1020 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1619 $ by $ \color{blue}{ 1020 } $ and get the remainder

$$ 1619 : 1020 = 1 \text{ ( remainder is } \color{blue}{ 599 } \text{ ) } $$

The remainder is still positive ($ 599 > 0 $), so we will continue with division.

Step 6 :
Divide $ 1020 $ by $ \color{blue}{ 599 } $ and get the remainder

$$ 1020 : 599 = 1 \text{ ( remainder is } \color{blue}{ 421 } \text{ ) } $$

The remainder is still positive ($ 421 > 0 $), so we will continue with division.

Step 7 :
Divide $ 599 $ by $ \color{blue}{ 421 } $ and get the remainder

$$ 599 : 421 = 1 \text{ ( remainder is } \color{blue}{ 178 } \text{ ) } $$

The remainder is still positive ($ 178 > 0 $), so we will continue with division.

Step 8 :
Divide $ 421 $ by $ \color{blue}{ 178 } $ and get the remainder

$$ 421 : 178 = 2 \text{ ( remainder is } \color{blue}{ 65 } \text{ ) } $$

The remainder is still positive ($ 65 > 0 $), so we will continue with division.

Step 9 :
Divide $ 178 $ by $ \color{blue}{ 65 } $ and get the remainder

$$ 178 : 65 = 2 \text{ ( remainder is } \color{blue}{ 48 } \text{ ) } $$

The remainder is still positive ($ 48 > 0 $), so we will continue with division.

Step 10 :
Divide $ 65 $ by $ \color{blue}{ 48 } $ and get the remainder

$$ 65 : 48 = 1 \text{ ( remainder is } \color{blue}{ 17 } \text{ ) } $$

The remainder is still positive ($ 17 > 0 $), so we will continue with division.

Step 11 :
Divide $ 48 $ by $ \color{blue}{ 17 } $ and get the remainder

$$ 48 : 17 = 2 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 12 :
Divide $ 17 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 17 : 14 = 1 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 13 :
Divide $ 14 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 14 : 3 = 4 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is still positive ($ 2 > 0 $), so we will continue with division.

Step 14 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 3 : 2 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

The remainder is still positive ($ 1 > 0 $), so we will continue with division.

Step 15 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

This solution can be visualized using a Venn diagram.

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

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