Step 1 :
Divide $ 16770 $ by $ 11770 $ and get the remainder

$$ 16770 : 11770 = 1 \text{ ( remainder is } \color{blue}{ 5000 } \text{ ) } $$

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

Step 2 :
Divide $ 11770 $ by $ \color{blue}{ 5000 } $ and get the remainder

$$ 11770 : 5000 = 2 \text{ ( remainder is } \color{blue}{ 1770 } \text{ ) } $$

The remainder is still positive ($ 1770 > 0 $), so we will continue with division.

Step 3 :
Divide $ 5000 $ by $ \color{blue}{ 1770 } $ and get the remainder

$$ 5000 : 1770 = 2 \text{ ( remainder is } \color{blue}{ 1460 } \text{ ) } $$

The remainder is still positive ($ 1460 > 0 $), so we will continue with division.

Step 4 :
Divide $ 1770 $ by $ \color{blue}{ 1460 } $ and get the remainder

$$ 1770 : 1460 = 1 \text{ ( remainder is } \color{blue}{ 310 } \text{ ) } $$

The remainder is still positive ($ 310 > 0 $), so we will continue with division.

Step 5 :
Divide $ 1460 $ by $ \color{blue}{ 310 } $ and get the remainder

$$ 1460 : 310 = 4 \text{ ( remainder is } \color{blue}{ 220 } \text{ ) } $$

The remainder is still positive ($ 220 > 0 $), so we will continue with division.

Step 6 :
Divide $ 310 $ by $ \color{blue}{ 220 } $ and get the remainder

$$ 310 : 220 = 1 \text{ ( remainder is } \color{blue}{ 90 } \text{ ) } $$

The remainder is still positive ($ 90 > 0 $), so we will continue with division.

Step 7 :
Divide $ 220 $ by $ \color{blue}{ 90 } $ and get the remainder

$$ 220 : 90 = 2 \text{ ( remainder is } \color{blue}{ 40 } \text{ ) } $$

The remainder is still positive ($ 40 > 0 $), so we will continue with division.

Step 8 :
Divide $ 90 $ by $ \color{blue}{ 40 } $ and get the remainder

$$ 90 : 40 = 2 \text{ ( remainder is } \color{blue}{ 10 } \text{ ) } $$

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

Step 9 :
Divide $ 40 $ by $ \color{blue}{ 10 } $ and get the remainder

$$ 40 : \color{blue}{ \boxed { 10 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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