Find Greatest Common Divisor of 60800 and 60200, using Euclidean algorithm.

Answer

The GCD of given numbers is 200.

Step 1 :
Divide $ 60800 $ by $ 60200 $ and get the remainder

$$ 60800 : 60200 = 1 \text{ ( remainder is } \color{blue}{ 600 } \text{ ) } $$

The remainder is positive ($ 600 > 0 $), so we will continue with division.

Step 2 :
Divide $ 60200 $ by $ \color{blue}{ 600 } $ and get the remainder

$$ 60200 : 600 = 100 \text{ ( remainder is } \color{blue}{ 200 } \text{ ) } $$

The remainder is still positive ($ 200 > 0 $), so we will continue with division.

Step 3 :
Divide $ 600 $ by $ \color{blue}{ 200 } $ and get the remainder

$$ 600 : \color{blue}{ \boxed { 200 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 200 }} $.

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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