Step 1 :
Divide $ 141 $ by $ 91 $ and get the remainder

$$ 141 : 91 = 1 \text{ ( remainder is } \color{blue}{ 50 } \text{ ) } $$

The remainder is positive ($ 50 > 0 $), so we will continue with division.

Step 2 :
Divide $ 91 $ by $ \color{blue}{ 50 } $ and get the remainder

$$ 91 : 50 = 1 \text{ ( remainder is } \color{blue}{ 41 } \text{ ) } $$

The remainder is still positive ($ 41 > 0 $), so we will continue with division.

Step 3 :
Divide $ 50 $ by $ \color{blue}{ 41 } $ and get the remainder

$$ 50 : 41 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 4 :
Divide $ 41 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 41 : 9 = 4 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

The remainder is still positive ($ 5 > 0 $), so we will continue with division.

Step 5 :
Divide $ 9 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 9 : 5 = 1 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 6 :
Divide $ 5 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 5 : 4 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 1 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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