Find Greatest Common Divisor of 1999 and 1090909, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1090909 $ by $ 1999 $ and get the remainder
The remainder is positive ($ 1454 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1999 $ by $ \color{blue}{ 1454 } $ and get the remainder
The remainder is still positive ($ 545 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1454 $ by $ \color{blue}{ 545 } $ and get the remainder
The remainder is still positive ($ 364 > 0 $), so we will continue with division.
Step 4 :
Divide $ 545 $ by $ \color{blue}{ 364 } $ and get the remainder
The remainder is still positive ($ 181 > 0 $), so we will continue with division.
Step 5 :
Divide $ 364 $ by $ \color{blue}{ 181 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 181 $ 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.
| 1090909 | : | 1999 | = | 545 | remainder ( 1454 ) | ||||||||||||
| 1999 | : | 1454 | = | 1 | remainder ( 545 ) | ||||||||||||
| 1454 | : | 545 | = | 2 | remainder ( 364 ) | ||||||||||||
| 545 | : | 364 | = | 1 | remainder ( 181 ) | ||||||||||||
| 364 | : | 181 | = | 2 | remainder ( 2 ) | ||||||||||||
| 181 | : | 2 | = | 90 | 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.