Find Greatest Common Divisor of 1147 and 889, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1147 $ by $ 889 $ and get the remainder
The remainder is positive ($ 258 > 0 $), so we will continue with division.
Step 2 :
Divide $ 889 $ by $ \color{blue}{ 258 } $ and get the remainder
The remainder is still positive ($ 115 > 0 $), so we will continue with division.
Step 3 :
Divide $ 258 $ by $ \color{blue}{ 115 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 4 :
Divide $ 115 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 28 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 3 $ 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.
| 1147 | : | 889 | = | 1 | remainder ( 258 ) | ||||||||||
| 889 | : | 258 | = | 3 | remainder ( 115 ) | ||||||||||
| 258 | : | 115 | = | 2 | remainder ( 28 ) | ||||||||||
| 115 | : | 28 | = | 4 | remainder ( 3 ) | ||||||||||
| 28 | : | 3 | = | 9 | remainder ( 1 ) | ||||||||||
| 3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||||||
| GCD = 1 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.