Find Greatest Common Divisor of 86 and 47, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 86 $ by $ 47 $ and get the remainder
The remainder is positive ($ 39 > 0 $), so we will continue with division.
Step 2 :
Divide $ 47 $ by $ \color{blue}{ 39 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 3 :
Divide $ 39 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 4 :
Divide $ 8 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 7 $ 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.
| 86 | : | 47 | = | 1 | remainder ( 39 ) | ||||||||
| 47 | : | 39 | = | 1 | remainder ( 8 ) | ||||||||
| 39 | : | 8 | = | 4 | remainder ( 7 ) | ||||||||
| 8 | : | 7 | = | 1 | remainder ( 1 ) | ||||||||
| 7 | : | 1 | = | 7 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.