Find Greatest Common Divisor of 605 and 210, using Euclidean algorithm.
Answer
The GCD of given numbers is 5.
Explanation
Step 1 :
Divide $ 605 $ by $ 210 $ and get the remainder
The remainder is positive ($ 185 > 0 $), so we will continue with division.
Step 2 :
Divide $ 210 $ by $ \color{blue}{ 185 } $ and get the remainder
The remainder is still positive ($ 25 > 0 $), so we will continue with division.
Step 3 :
Divide $ 185 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 25 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 5 :
Divide $ 10 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 5 }} $.
We can summarize an algorithm into a following table.
| 605 | : | 210 | = | 2 | remainder ( 185 ) | ||||||||
| 210 | : | 185 | = | 1 | remainder ( 25 ) | ||||||||
| 185 | : | 25 | = | 7 | remainder ( 10 ) | ||||||||
| 25 | : | 10 | = | 2 | remainder ( 5 ) | ||||||||
| 10 | : | 5 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 5 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.