Find Greatest Common Divisor of 20 and 67, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 67 $ by $ 20 $ and get the remainder
The remainder is positive ($ 7 > 0 $), so we will continue with division.
Step 2 :
Divide $ 20 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 3 :
Divide $ 7 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 6 $ 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.
| 67 | : | 20 | = | 3 | remainder ( 7 ) | ||||||
| 20 | : | 7 | = | 2 | remainder ( 6 ) | ||||||
| 7 | : | 6 | = | 1 | remainder ( 1 ) | ||||||
| 6 | : | 1 | = | 6 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.