Step 1 :
Divide $ 3731 $ by $ 239 $ and get the remainder

$$ 3731 : 239 = 15 \text{ ( remainder is } \color{blue}{ 146 } \text{ ) } $$

The remainder is positive ($ 146 > 0 $), so we will continue with division.

Step 2 :
Divide $ 239 $ by $ \color{blue}{ 146 } $ and get the remainder

$$ 239 : 146 = 1 \text{ ( remainder is } \color{blue}{ 93 } \text{ ) } $$

The remainder is still positive ($ 93 > 0 $), so we will continue with division.

Step 3 :
Divide $ 146 $ by $ \color{blue}{ 93 } $ and get the remainder

$$ 146 : 93 = 1 \text{ ( remainder is } \color{blue}{ 53 } \text{ ) } $$

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

Step 4 :
Divide $ 93 $ by $ \color{blue}{ 53 } $ and get the remainder

$$ 93 : 53 = 1 \text{ ( remainder is } \color{blue}{ 40 } \text{ ) } $$

The remainder is still positive ($ 40 > 0 $), so we will continue with division.

Step 5 :
Divide $ 53 $ by $ \color{blue}{ 40 } $ and get the remainder

$$ 53 : 40 = 1 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 6 :
Divide $ 40 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 40 : 13 = 3 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 13 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 13 : \color{blue}{ \boxed { 1 }} = 13 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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