Find Greatest Common Divisor of 114 and 324, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 324 $ by $ 114 $ and get the remainder
The remainder is positive ($ 96 > 0 $), so we will continue with division.
Step 2 :
Divide $ 114 $ by $ \color{blue}{ 96 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 3 :
Divide $ 96 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 18 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
| 324 | : | 114 | = | 2 | remainder ( 96 ) | ||||||
| 114 | : | 96 | = | 1 | remainder ( 18 ) | ||||||
| 96 | : | 18 | = | 5 | remainder ( 6 ) | ||||||
| 18 | : | 6 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 6 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.