Step 1 :
Divide $ 7765 $ by $ 756 $ and get the remainder

$$ 7765 : 756 = 10 \text{ ( remainder is } \color{blue}{ 205 } \text{ ) } $$

The remainder is positive ($ 205 > 0 $), so we will continue with division.

Step 2 :
Divide $ 756 $ by $ \color{blue}{ 205 } $ and get the remainder

$$ 756 : 205 = 3 \text{ ( remainder is } \color{blue}{ 141 } \text{ ) } $$

The remainder is still positive ($ 141 > 0 $), so we will continue with division.

Step 3 :
Divide $ 205 $ by $ \color{blue}{ 141 } $ and get the remainder

$$ 205 : 141 = 1 \text{ ( remainder is } \color{blue}{ 64 } \text{ ) } $$

The remainder is still positive ($ 64 > 0 $), so we will continue with division.

Step 4 :
Divide $ 141 $ by $ \color{blue}{ 64 } $ and get the remainder

$$ 141 : 64 = 2 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

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

Step 5 :
Divide $ 64 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 64 : 13 = 4 \text{ ( remainder is } \color{blue}{ 12 } \text{ ) } $$

The remainder is still positive ($ 12 > 0 $), so we will continue with division.

Step 6 :
Divide $ 13 $ by $ \color{blue}{ 12 } $ and get the remainder

$$ 13 : 12 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 7 :
Divide $ 12 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 12 : \color{blue}{ \boxed { 1 }} = 12 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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