Step 1 :
Divide $ 2191 $ by $ 1351 $ and get the remainder

$$ 2191 : 1351 = 1 \text{ ( remainder is } \color{blue}{ 840 } \text{ ) } $$

The remainder is positive ($ 840 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1351 $ by $ \color{blue}{ 840 } $ and get the remainder

$$ 1351 : 840 = 1 \text{ ( remainder is } \color{blue}{ 511 } \text{ ) } $$

The remainder is still positive ($ 511 > 0 $), so we will continue with division.

Step 3 :
Divide $ 840 $ by $ \color{blue}{ 511 } $ and get the remainder

$$ 840 : 511 = 1 \text{ ( remainder is } \color{blue}{ 329 } \text{ ) } $$

The remainder is still positive ($ 329 > 0 $), so we will continue with division.

Step 4 :
Divide $ 511 $ by $ \color{blue}{ 329 } $ and get the remainder

$$ 511 : 329 = 1 \text{ ( remainder is } \color{blue}{ 182 } \text{ ) } $$

The remainder is still positive ($ 182 > 0 $), so we will continue with division.

Step 5 :
Divide $ 329 $ by $ \color{blue}{ 182 } $ and get the remainder

$$ 329 : 182 = 1 \text{ ( remainder is } \color{blue}{ 147 } \text{ ) } $$

The remainder is still positive ($ 147 > 0 $), so we will continue with division.

Step 6 :
Divide $ 182 $ by $ \color{blue}{ 147 } $ and get the remainder

$$ 182 : 147 = 1 \text{ ( remainder is } \color{blue}{ 35 } \text{ ) } $$

The remainder is still positive ($ 35 > 0 $), so we will continue with division.

Step 7 :
Divide $ 147 $ by $ \color{blue}{ 35 } $ and get the remainder

$$ 147 : 35 = 4 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 8 :
Divide $ 35 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 35 : \color{blue}{ \boxed { 7 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.

This solution can be visualized using a Venn diagram.

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

GCD Calculator