Find Greatest Common Divisor of 200000001 and 200000003, using Euclidean algorithm.

Answer

The GCD of given numbers is 1.

Step 1 :
Divide $ 200000003 $ by $ 200000001 $ and get the remainder

$$ 200000003 : 200000001 = 1 \text{ ( remainder is } \color{blue}{ 2 } \text{ ) } $$

The remainder is positive ($ 2 > 0 $), so we will continue with division.

Step 2 :
Divide $ 200000001 $ by $ \color{blue}{ 2 } $ and get the remainder

$$ 200000001 : 2 = 100000000 \text{ ( remainder is } \color{blue}{ 1 } \text{ ) } $$

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

Step 3 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder

$$ 2 : \color{blue}{ \boxed { 1 }} = 2 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

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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