Step 1 :
Divide $ 15770 $ by $ 10770 $ and get the remainder

$$ 15770 : 10770 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

The remainder is positive ($ 5000 > 0 $), so we will continue with division.

Step 2 :
Divide $ 10770 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 10770 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 770 } \text{ ) } $$

The remainder is still positive ($ 770 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 770 } $ and get the remainder

$$ 5000 : 770 = 6 \text{ ( remainder is } \color{blue}{ 380 } \text{ ) } $$

The remainder is still positive ($ 380 > 0 $), so we will continue with division.

Step 4 :
Divide $ 770 $ by $ \color{blue}{ 380 } $ and get the remainder

$$ 770 : 380 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

The remainder is still positive ($ 10 > 0 $), so we will continue with division.

Step 5 :
Divide $ 380 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 380 : \color{blue}{ \boxed { 10 }} = 38 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.

This solution can be visualized using a Venn diagram.

The GCD equals the product of the numbers at the intersection.

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