Find Greatest Common Divisor of 71 and 83, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 83 $ by $ 71 $ and get the remainder
The remainder is positive ($ 12 > 0 $), so we will continue with division.
Step 2 :
Divide $ 71 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 3 :
Divide $ 12 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 11 $ 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.
| 83 | : | 71 | = | 1 | remainder ( 12 ) | ||||||
| 71 | : | 12 | = | 5 | remainder ( 11 ) | ||||||
| 12 | : | 11 | = | 1 | remainder ( 1 ) | ||||||
| 11 | : | 1 | = | 11 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.