Find Greatest Common Divisor of 90 and 67, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 90 $ by $ 67 $ and get the remainder
The remainder is positive ($ 23 > 0 $), so we will continue with division.
Step 2 :
Divide $ 67 $ by $ \color{blue}{ 23 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 3 :
Divide $ 23 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 4 :
Divide $ 21 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 2 $ 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.
| 90 | : | 67 | = | 1 | remainder ( 23 ) | ||||||||
| 67 | : | 23 | = | 2 | remainder ( 21 ) | ||||||||
| 23 | : | 21 | = | 1 | remainder ( 2 ) | ||||||||
| 21 | : | 2 | = | 10 | remainder ( 1 ) | ||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.