Find Greatest Common Divisor of 55 and 41, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 55 $ by $ 41 $ and get the remainder
The remainder is positive ($ 14 > 0 $), so we will continue with division.
Step 2 :
Divide $ 41 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 3 :
Divide $ 14 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 13 $ 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.
| 55 | : | 41 | = | 1 | remainder ( 14 ) | ||||||
| 41 | : | 14 | = | 2 | remainder ( 13 ) | ||||||
| 14 | : | 13 | = | 1 | remainder ( 1 ) | ||||||
| 13 | : | 1 | = | 13 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.