Find Greatest Common Divisor of 210 and 588, using Euclidean algorithm.

Answer

The GCD of given numbers is 42.

Step 1 :
Divide $ 588 $ by $ 210 $ and get the remainder

$$ 588 : 210 = 2 \text{ ( remainder is } \color{blue}{ 168 } \text{ ) } $$

The remainder is positive ($ 168 > 0 $), so we will continue with division.

Step 2 :
Divide $ 210 $ by $ \color{blue}{ 168 } $ and get the remainder

$$ 210 : 168 = 1 \text{ ( remainder is } \color{blue}{ 42 } \text{ ) } $$

The remainder is still positive ($ 42 > 0 $), so we will continue with division.

Step 3 :
Divide $ 168 $ by $ \color{blue}{ 42 } $ and get the remainder

$$ 168 : \color{blue}{ \boxed { 42 }} = 4 \text{ ( remainder is } \color{blue}{ 0 } \text{ ) } $$

The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 42 }} $.

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.

This page was created using

GCD Calculator