Find Greatest Common Divisor of 123 and 297, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 297 $ by $ 123 $ and get the remainder
The remainder is positive ($ 51 > 0 $), so we will continue with division.
Step 2 :
Divide $ 123 $ by $ \color{blue}{ 51 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 3 :
Divide $ 51 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 4 :
Divide $ 21 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 9 $ 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.
| 297 | : | 123 | = | 2 | remainder ( 51 ) | ||||||||
| 123 | : | 51 | = | 2 | remainder ( 21 ) | ||||||||
| 51 | : | 21 | = | 2 | remainder ( 9 ) | ||||||||
| 21 | : | 9 | = | 2 | remainder ( 3 ) | ||||||||
| 9 | : | 3 | = | 3 | remainder ( 0 ) | ||||||||
| GCD = 3 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.