Find Greatest Common Divisor of 419 and 105, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Step 1 :
Divide $ 419 $ by $ 105 $ and get the remainder

$$ 419 : 105 = 3 \text{ ( remainder is } \color{blue}{ 104 } \text{ ) } $$

The remainder is positive ($ 104 > 0 $), so we will continue with division.

Step 2 :
Divide $ 105 $ by $ \color{blue}{ 104 } $ and get the remainder

$$ 105 : 104 = 1 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 3 :
Divide $ 104 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 104 : \color{blue}{ \boxed { 1 }} = 104 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.

We can summarize an algorithm into a following table.

This solution can be visualized using a Venn diagram.

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

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