Step 1 :
Divide $ 785 $ by $ 102 $ and get the remainder

$$ 785 : 102 = 7 \text{ ( remainder is } \color{blue}{ 71 } \text{ ) } $$

The remainder is positive ($ 71 > 0 $), so we will continue with division.

Step 2 :
Divide $ 102 $ by $ \color{blue}{ 71 } $ and get the remainder

$$ 102 : 71 = 1 \text{ ( remainder is } \color{blue}{ 31 } \text{ ) } $$

The remainder is still positive ($ 31 > 0 $), so we will continue with division.

Step 3 :
Divide $ 71 $ by $ \color{blue}{ 31 } $ and get the remainder

$$ 71 : 31 = 2 \text{ ( remainder is } \color{blue}{ 9 } \text{ ) } $$

The remainder is still positive ($ 9 > 0 $), so we will continue with division.

Step 4 :
Divide $ 31 $ by $ \color{blue}{ 9 } $ and get the remainder

$$ 31 : 9 = 3 \text{ ( remainder is } \color{blue}{ 4 } \text{ ) } $$

The remainder is still positive ($ 4 > 0 $), so we will continue with division.

Step 5 :
Divide $ 9 $ by $ \color{blue}{ 4 } $ and get the remainder

$$ 9 : 4 = 2 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 4 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 4 : \color{blue}{ \boxed { 1 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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