Find Greatest Common Divisor of 1769 and 2378, using Euclidean algorithm.
Answer
The GCD of given numbers is 29.
Explanation
Step 1 :
Divide $ 2378 $ by $ 1769 $ and get the remainder
The remainder is positive ($ 609 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1769 $ by $ \color{blue}{ 609 } $ and get the remainder
The remainder is still positive ($ 551 > 0 $), so we will continue with division.
Step 3 :
Divide $ 609 $ by $ \color{blue}{ 551 } $ and get the remainder
The remainder is still positive ($ 58 > 0 $), so we will continue with division.
Step 4 :
Divide $ 551 $ by $ \color{blue}{ 58 } $ and get the remainder
The remainder is still positive ($ 29 > 0 $), so we will continue with division.
Step 5 :
Divide $ 58 $ by $ \color{blue}{ 29 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 29 }} $.
We can summarize an algorithm into a following table.
| 2378 | : | 1769 | = | 1 | remainder ( 609 ) | ||||||||
| 1769 | : | 609 | = | 2 | remainder ( 551 ) | ||||||||
| 609 | : | 551 | = | 1 | remainder ( 58 ) | ||||||||
| 551 | : | 58 | = | 9 | remainder ( 29 ) | ||||||||
| 58 | : | 29 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 29 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.