Find Greatest Common Divisor of 77 and 30, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 77 $ by $ 30 $ and get the remainder
The remainder is positive ($ 17 > 0 $), so we will continue with division.
Step 2 :
Divide $ 30 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is still positive ($ 13 > 0 $), so we will continue with division.
Step 3 :
Divide $ 17 $ by $ \color{blue}{ 13 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
Divide $ 13 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 4 $ 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.
| 77 | : | 30 | = | 2 | remainder ( 17 ) | ||||||||
| 30 | : | 17 | = | 1 | remainder ( 13 ) | ||||||||
| 17 | : | 13 | = | 1 | remainder ( 4 ) | ||||||||
| 13 | : | 4 | = | 3 | remainder ( 1 ) | ||||||||
| 4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||||
| GCD = 1 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.