Find Greatest Common Divisor of 671 and 77, using Euclidean algorithm.
Answer
The GCD of given numbers is 11.
Explanation
Step 1 :
Divide $ 671 $ by $ 77 $ and get the remainder
The remainder is positive ($ 55 > 0 $), so we will continue with division.
Step 2 :
Divide $ 77 $ by $ \color{blue}{ 55 } $ and get the remainder
The remainder is still positive ($ 22 > 0 $), so we will continue with division.
Step 3 :
Divide $ 55 $ by $ \color{blue}{ 22 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 4 :
Divide $ 22 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 11 }} $.
We can summarize an algorithm into a following table.
| 671 | : | 77 | = | 8 | remainder ( 55 ) | ||||||
| 77 | : | 55 | = | 1 | remainder ( 22 ) | ||||||
| 55 | : | 22 | = | 2 | remainder ( 11 ) | ||||||
| 22 | : | 11 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 11 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.