Step 1 :
Divide $ 11743 $ by $ 1226 $ and get the remainder

$$ 11743 : 1226 = 9 \text{ ( remainder is } \color{blue}{ 709 } \text{ ) } $$

The remainder is positive ($ 709 > 0 $), so we will continue with division.

Step 2 :
Divide $ 1226 $ by $ \color{blue}{ 709 } $ and get the remainder

$$ 1226 : 709 = 1 \text{ ( remainder is } \color{blue}{ 517 } \text{ ) } $$

The remainder is still positive ($ 517 > 0 $), so we will continue with division.

Step 3 :
Divide $ 709 $ by $ \color{blue}{ 517 } $ and get the remainder

$$ 709 : 517 = 1 \text{ ( remainder is } \color{blue}{ 192 } \text{ ) } $$

The remainder is still positive ($ 192 > 0 $), so we will continue with division.

Step 4 :
Divide $ 517 $ by $ \color{blue}{ 192 } $ and get the remainder

$$ 517 : 192 = 2 \text{ ( remainder is } \color{blue}{ 133 } \text{ ) } $$

The remainder is still positive ($ 133 > 0 $), so we will continue with division.

Step 5 :
Divide $ 192 $ by $ \color{blue}{ 133 } $ and get the remainder

$$ 192 : 133 = 1 \text{ ( remainder is } \color{blue}{ 59 } \text{ ) } $$

The remainder is still positive ($ 59 > 0 $), so we will continue with division.

Step 6 :
Divide $ 133 $ by $ \color{blue}{ 59 } $ and get the remainder

$$ 133 : 59 = 2 \text{ ( remainder is } \color{blue}{ 15 } \text{ ) } $$

The remainder is still positive ($ 15 > 0 $), so we will continue with division.

Step 7 :
Divide $ 59 $ by $ \color{blue}{ 15 } $ and get the remainder

$$ 59 : 15 = 3 \text{ ( remainder is } \color{blue}{ 14 } \text{ ) } $$

The remainder is still positive ($ 14 > 0 $), so we will continue with division.

Step 8 :
Divide $ 15 $ by $ \color{blue}{ 14 } $ and get the remainder

$$ 15 : 14 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 9 :
Divide $ 14 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 14 : \color{blue}{ \boxed { 1 }} = 14 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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