Step 1 :
Divide $ 9103 $ by $ 2365 $ and get the remainder

$$ 9103 : 2365 = 3 \text{ ( remainder is } \color{blue}{ 2008 } \text{ ) } $$

The remainder is positive ($ 2008 > 0 $), so we will continue with division.

Step 2 :
Divide $ 2365 $ by $ \color{blue}{ 2008 } $ and get the remainder

$$ 2365 : 2008 = 1 \text{ ( remainder is } \color{blue}{ 357 } \text{ ) } $$

The remainder is still positive ($ 357 > 0 $), so we will continue with division.

Step 3 :
Divide $ 2008 $ by $ \color{blue}{ 357 } $ and get the remainder

$$ 2008 : 357 = 5 \text{ ( remainder is } \color{blue}{ 223 } \text{ ) } $$

The remainder is still positive ($ 223 > 0 $), so we will continue with division.

Step 4 :
Divide $ 357 $ by $ \color{blue}{ 223 } $ and get the remainder

$$ 357 : 223 = 1 \text{ ( remainder is } \color{blue}{ 134 } \text{ ) } $$

The remainder is still positive ($ 134 > 0 $), so we will continue with division.

Step 5 :
Divide $ 223 $ by $ \color{blue}{ 134 } $ and get the remainder

$$ 223 : 134 = 1 \text{ ( remainder is } \color{blue}{ 89 } \text{ ) } $$

The remainder is still positive ($ 89 > 0 $), so we will continue with division.

Step 6 :
Divide $ 134 $ by $ \color{blue}{ 89 } $ and get the remainder

$$ 134 : 89 = 1 \text{ ( remainder is } \color{blue}{ 45 } \text{ ) } $$

The remainder is still positive ($ 45 > 0 $), so we will continue with division.

Step 7 :
Divide $ 89 $ by $ \color{blue}{ 45 } $ and get the remainder

$$ 89 : 45 = 1 \text{ ( remainder is } \color{blue}{ 44 } \text{ ) } $$

The remainder is still positive ($ 44 > 0 $), so we will continue with division.

Step 8 :
Divide $ 45 $ by $ \color{blue}{ 44 } $ and get the remainder

$$ 45 : 44 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 9 :
Divide $ 44 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 44 : \color{blue}{ \boxed { 1 }} = 44 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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