Find Greatest Common Divisor of 509 and 1177, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1177 $ by $ 509 $ and get the remainder
The remainder is positive ($ 159 > 0 $), so we will continue with division.
Step 2 :
Divide $ 509 $ by $ \color{blue}{ 159 } $ and get the remainder
The remainder is still positive ($ 32 > 0 $), so we will continue with division.
Step 3 :
Divide $ 159 $ by $ \color{blue}{ 32 } $ and get the remainder
The remainder is still positive ($ 31 > 0 $), so we will continue with division.
Step 4 :
Divide $ 32 $ by $ \color{blue}{ 31 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 31 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 1177 | : | 509 | = | 2 | remainder ( 159 ) | ||||||||
| 509 | : | 159 | = | 3 | remainder ( 32 ) | ||||||||
| 159 | : | 32 | = | 4 | remainder ( 31 ) | ||||||||
| 32 | : | 31 | = | 1 | remainder ( 1 ) | ||||||||
| 31 | : | 1 | = | 31 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.