Step 1 :
Divide $ 8441 $ by $ 137 $ and get the remainder

$$ 8441 : 137 = 61 \text{ ( remainder is } \color{blue}{ 84 } \text{ ) } $$

The remainder is positive ($ 84 > 0 $), so we will continue with division.

Step 2 :
Divide $ 137 $ by $ \color{blue}{ 84 } $ and get the remainder

$$ 137 : 84 = 1 \text{ ( remainder is } \color{blue}{ 53 } \text{ ) } $$

The remainder is still positive ($ 53 > 0 $), so we will continue with division.

Step 3 :
Divide $ 84 $ by $ \color{blue}{ 53 } $ and get the remainder

$$ 84 : 53 = 1 \text{ ( remainder is } \color{blue}{ 31 } \text{ ) } $$

The remainder is still positive ($ 31 > 0 $), so we will continue with division.

Step 4 :
Divide $ 53 $ by $ \color{blue}{ 31 } $ and get the remainder

$$ 53 : 31 = 1 \text{ ( remainder is } \color{blue}{ 22 } \text{ ) } $$

The remainder is still positive ($ 22 > 0 $), so we will continue with division.

Step 5 :
Divide $ 31 $ by $ \color{blue}{ 22 } $ and get the remainder

$$ 31 : 22 = 1 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

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

Step 6 :
Divide $ 22 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 22 : 9 = 2 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

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

Step 7 :
Divide $ 9 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 9 : 4 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 8 :
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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