Step 1 :
Divide $ 1870 $ by $ 261 $ and get the remainder

$$ 1870 : 261 = 7 \text{ ( remainder is } \color{blue}{ 43 } \text{ ) } $$

The remainder is positive ($ 43 > 0 $), so we will continue with division.

Step 2 :
Divide $ 261 $ by $ \color{blue}{ 43 } $ and get the remainder

$$ 261 : 43 = 6 \text{ ( remainder is } \color{blue}{ 3 } \text{ ) } $$

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

Step 3 :
Divide $ 43 $ by $ \color{blue}{ 3 } $ and get the remainder

$$ 43 : 3 = 14 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 4 :
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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