Step 1 :
Divide $ 1879 $ by $ 460 $ and get the remainder

$$ 1879 : 460 = 4 \text{ ( remainder is } \color{blue}{ 39 } \text{ ) } $$

The remainder is positive ($ 39 > 0 $), so we will continue with division.

Step 2 :
Divide $ 460 $ by $ \color{blue}{ 39 } $ and get the remainder

$$ 460 : 39 = 11 \text{ ( remainder is } \color{blue}{ 31 } \text{ ) } $$

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

Step 3 :
Divide $ 39 $ by $ \color{blue}{ 31 } $ and get the remainder

$$ 39 : 31 = 1 \text{ ( remainder is } \color{blue}{ 8 } \text{ ) } $$

The remainder is still positive ($ 8 > 0 $), so we will continue with division.

Step 4 :
Divide $ 31 $ by $ \color{blue}{ 8 } $ and get the remainder

$$ 31 : 8 = 3 \text{ ( remainder is } \color{blue}{ 7 } \text{ ) } $$

The remainder is still positive ($ 7 > 0 $), so we will continue with division.

Step 5 :
Divide $ 8 $ by $ \color{blue}{ 7 } $ and get the remainder

$$ 8 : 7 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 6 :
Divide $ 7 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 7 : \color{blue}{ \boxed { 1 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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