Step 1 :
Divide $ 3255854716 $ by $ 65537 $ and get the remainder

$$ 3255854716 : 65537 = 49679 \text{ ( remainder is } \color{blue}{ 42093 } \text{ ) } $$

The remainder is positive ($ 42093 > 0 $), so we will continue with division.

Step 2 :
Divide $ 65537 $ by $ \color{blue}{ 42093 } $ and get the remainder

$$ 65537 : 42093 = 1 \text{ ( remainder is } \color{blue}{ 23444 } \text{ ) } $$

The remainder is still positive ($ 23444 > 0 $), so we will continue with division.

Step 3 :
Divide $ 42093 $ by $ \color{blue}{ 23444 } $ and get the remainder

$$ 42093 : 23444 = 1 \text{ ( remainder is } \color{blue}{ 18649 } \text{ ) } $$

The remainder is still positive ($ 18649 > 0 $), so we will continue with division.

Step 4 :
Divide $ 23444 $ by $ \color{blue}{ 18649 } $ and get the remainder

$$ 23444 : 18649 = 1 \text{ ( remainder is } \color{blue}{ 4795 } \text{ ) } $$

The remainder is still positive ($ 4795 > 0 $), so we will continue with division.

Step 5 :
Divide $ 18649 $ by $ \color{blue}{ 4795 } $ and get the remainder

$$ 18649 : 4795 = 3 \text{ ( remainder is } \color{blue}{ 4264 } \text{ ) } $$

The remainder is still positive ($ 4264 > 0 $), so we will continue with division.

Step 6 :
Divide $ 4795 $ by $ \color{blue}{ 4264 } $ and get the remainder

$$ 4795 : 4264 = 1 \text{ ( remainder is } \color{blue}{ 531 } \text{ ) } $$

The remainder is still positive ($ 531 > 0 $), so we will continue with division.

Step 7 :
Divide $ 4264 $ by $ \color{blue}{ 531 } $ and get the remainder

$$ 4264 : 531 = 8 \text{ ( remainder is } \color{blue}{ 16 } \text{ ) } $$

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

Step 8 :
Divide $ 531 $ by $ \color{blue}{ 16 } $ and get the remainder

$$ 531 : 16 = 33 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

The remainder is still positive ($ 3 > 0 $), so we will continue with division.

Step 9 :
Divide $ 16 $ by $ \color{blue}{ 3 } $ and get the remainder

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

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

Step 10 :
Divide $ 3 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 3 : \color{blue}{ \boxed { 1 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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