Step 1 :
Divide $ 131718 $ by $ 7241 $ and get the remainder

$$ 131718 : 7241 = 18 \text{ ( remainder is } \color{blue}{ 1380 } \text{ ) } $$

The remainder is positive ($ 1380 > 0 $), so we will continue with division.

Step 2 :
Divide $ 7241 $ by $ \color{blue}{ 1380 } $ and get the remainder

$$ 7241 : 1380 = 5 \text{ ( remainder is } \color{blue}{ 341 } \text{ ) } $$

The remainder is still positive ($ 341 > 0 $), so we will continue with division.

Step 3 :
Divide $ 1380 $ by $ \color{blue}{ 341 } $ and get the remainder

$$ 1380 : 341 = 4 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

The remainder is still positive ($ 16 > 0 $), so we will continue with division.

Step 4 :
Divide $ 341 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 341 : 16 = 21 \text{ ( remainder is } \color{blue}{ 5 } \text{ ) } $$

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

Step 5 :
Divide $ 16 $ by $ \color{blue}{ 5 } $ and get the remainder

$$ 16 : 5 = 3 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 5 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 5 : \color{blue}{ \boxed { 1 }} = 5 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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