Find Greatest Common Divisor of 97 and 29, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 97 $ by $ 29 $ and get the remainder
The remainder is positive ($ 10 > 0 $), so we will continue with division.
Step 2 :
Divide $ 29 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 3 :
Divide $ 10 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 9 $ 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.
| 97 | : | 29 | = | 3 | remainder ( 10 ) | ||||||
| 29 | : | 10 | = | 2 | remainder ( 9 ) | ||||||
| 10 | : | 9 | = | 1 | remainder ( 1 ) | ||||||
| 9 | : | 1 | = | 9 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.