Find Greatest Common Divisor of 585 and 169, using Euclidean algorithm.

Answer

The GCD of given numbers is 13.

Step 1 :
Divide $ 585 $ by $ 169 $ and get the remainder

$$ 585 : 169 = 3 \text{ ( remainder is } \color{blue}{ 78 } \text{ ) } $$

The remainder is positive ($ 78 > 0 $), so we will continue with division.

Step 2 :
Divide $ 169 $ by $ \color{blue}{ 78 } $ and get the remainder

$$ 169 : 78 = 2 \text{ ( remainder is } \color{blue}{ 13 } \text{ ) } $$

The remainder is still positive ($ 13 > 0 $), so we will continue with division.

Step 3 :
Divide $ 78 $ by $ \color{blue}{ 13 } $ and get the remainder

$$ 78 : \color{blue}{ \boxed { 13 }} = 6 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 13 }} $.

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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