Find Greatest Common Divisor of 1092 and 2295, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 2295 $ by $ 1092 $ and get the remainder
The remainder is positive ($ 111 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1092 $ by $ \color{blue}{ 111 } $ and get the remainder
The remainder is still positive ($ 93 > 0 $), so we will continue with division.
Step 3 :
Divide $ 111 $ by $ \color{blue}{ 93 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 4 :
Divide $ 93 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 18 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 2295 | : | 1092 | = | 2 | remainder ( 111 ) | ||||||||
| 1092 | : | 111 | = | 9 | remainder ( 93 ) | ||||||||
| 111 | : | 93 | = | 1 | remainder ( 18 ) | ||||||||
| 93 | : | 18 | = | 5 | remainder ( 3 ) | ||||||||
| 18 | : | 3 | = | 6 | remainder ( 0 ) | ||||||||
| GCD = 3 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.