Find Greatest Common Divisor of 506 and 2185, using Euclidean algorithm.

Answer

The GCD of given numbers is 23.

Step 1 :
Divide $ 2185 $ by $ 506 $ and get the remainder

$$ 2185 : 506 = 4 \text{ ( remainder is } \color{blue}{ 161 } \text{ ) } $$

The remainder is positive ($ 161 > 0 $), so we will continue with division.

Step 2 :
Divide $ 506 $ by $ \color{blue}{ 161 } $ and get the remainder

$$ 506 : 161 = 3 \text{ ( remainder is } \color{blue}{ 23 } \text{ ) } $$

The remainder is still positive ($ 23 > 0 $), so we will continue with division.

Step 3 :
Divide $ 161 $ by $ \color{blue}{ 23 } $ and get the remainder

$$ 161 : \color{blue}{ \boxed { 23 }} = 7 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 23 }} $.

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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