The GCD of given numbers is 117.
Step 1 :
Divide $ 585 $ by $ 234 $ and get the remainder
The remainder is positive ($ 117 > 0 $), so we will continue with division.
Step 2 :
Divide $ 234 $ by $ \color{blue}{ 117 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 117 }} $.
We can summarize an algorithm into a following table.
585 | : | 234 | = | 2 | remainder ( 117 ) | ||
234 | : | 117 | = | 2 | remainder ( 0 ) | ||
GCD = 117 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.