Find Greatest Common Divisor of 2286 and 2575, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 2575 $ by $ 2286 $ and get the remainder
The remainder is positive ($ 289 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2286 $ by $ \color{blue}{ 289 } $ and get the remainder
The remainder is still positive ($ 263 > 0 $), so we will continue with division.
Step 3 :
Divide $ 289 $ by $ \color{blue}{ 263 } $ and get the remainder
The remainder is still positive ($ 26 > 0 $), so we will continue with division.
Step 4 :
Divide $ 263 $ by $ \color{blue}{ 26 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 26 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
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.
| 2575 | : | 2286 | = | 1 | remainder ( 289 ) | ||||||||||||
| 2286 | : | 289 | = | 7 | remainder ( 263 ) | ||||||||||||
| 289 | : | 263 | = | 1 | remainder ( 26 ) | ||||||||||||
| 263 | : | 26 | = | 10 | remainder ( 3 ) | ||||||||||||
| 26 | : | 3 | = | 8 | remainder ( 2 ) | ||||||||||||
| 3 | : | 2 | = | 1 | 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.