Find Greatest Common Divisor of 34 and 57, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 57 $ by $ 34 $ and get the remainder
The remainder is positive ($ 23 > 0 $), so we will continue with division.
Step 2 :
Divide $ 34 $ by $ \color{blue}{ 23 } $ and get the remainder
The remainder is still positive ($ 11 > 0 $), so we will continue with division.
Step 3 :
Divide $ 23 $ by $ \color{blue}{ 11 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 11 $ 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.
| 57 | : | 34 | = | 1 | remainder ( 23 ) | ||||||
| 34 | : | 23 | = | 1 | remainder ( 11 ) | ||||||
| 23 | : | 11 | = | 2 | remainder ( 1 ) | ||||||
| 11 | : | 1 | = | 11 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.