Find Greatest Common Divisor of 578 and 489, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 578 $ by $ 489 $ and get the remainder
The remainder is positive ($ 89 > 0 $), so we will continue with division.
Step 2 :
Divide $ 489 $ by $ \color{blue}{ 89 } $ and get the remainder
The remainder is still positive ($ 44 > 0 $), so we will continue with division.
Step 3 :
Divide $ 89 $ by $ \color{blue}{ 44 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 44 $ 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.
| 578 | : | 489 | = | 1 | remainder ( 89 ) | ||||||
| 489 | : | 89 | = | 5 | remainder ( 44 ) | ||||||
| 89 | : | 44 | = | 2 | remainder ( 1 ) | ||||||
| 44 | : | 1 | = | 44 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.