Find Greatest Common Divisor of 260 and 455, using Euclidean algorithm.

Answer

The GCD of given numbers is 65.

Step 1 :
Divide $ 455 $ by $ 260 $ and get the remainder

$$ 455 : 260 = 1 \text{ ( remainder is } \color{blue}{ 195 } \text{ ) } $$

The remainder is positive ($ 195 > 0 $), so we will continue with division.

Step 2 :
Divide $ 260 $ by $ \color{blue}{ 195 } $ and get the remainder

$$ 260 : 195 = 1 \text{ ( remainder is } \color{blue}{ 65 } \text{ ) } $$

The remainder is still positive ($ 65 > 0 $), so we will continue with division.

Step 3 :
Divide $ 195 $ by $ \color{blue}{ 65 } $ and get the remainder

$$ 195 : \color{blue}{ \boxed { 65 }} = 3 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 65 }} $.

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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