Find Greatest Common Divisor of 391 and 667, using Euclidean algorithm.
Answer
The GCD of given numbers is 23.
Explanation
Step 1 :
Divide $ 667 $ by $ 391 $ and get the remainder
The remainder is positive ($ 276 > 0 $), so we will continue with division.
Step 2 :
Divide $ 391 $ by $ \color{blue}{ 276 } $ and get the remainder
The remainder is still positive ($ 115 > 0 $), so we will continue with division.
Step 3 :
Divide $ 276 $ by $ \color{blue}{ 115 } $ and get the remainder
The remainder is still positive ($ 46 > 0 $), so we will continue with division.
Step 4 :
Divide $ 115 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is still positive ($ 23 > 0 $), so we will continue with division.
Step 5 :
Divide $ 46 $ by $ \color{blue}{ 23 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 23 }} $.
We can summarize an algorithm into a following table.
| 667 | : | 391 | = | 1 | remainder ( 276 ) | ||||||||
| 391 | : | 276 | = | 1 | remainder ( 115 ) | ||||||||
| 276 | : | 115 | = | 2 | remainder ( 46 ) | ||||||||
| 115 | : | 46 | = | 2 | remainder ( 23 ) | ||||||||
| 46 | : | 23 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 23 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.