Find Greatest Common Divisor of 504 and 270, using Euclidean algorithm.
Answer
The GCD of given numbers is 18.
Explanation
Step 1 :
Divide $ 504 $ by $ 270 $ and get the remainder
The remainder is positive ($ 234 > 0 $), so we will continue with division.
Step 2 :
Divide $ 270 $ by $ \color{blue}{ 234 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 3 :
Divide $ 234 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 4 :
Divide $ 36 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 18 }} $.
We can summarize an algorithm into a following table.
| 504 | : | 270 | = | 1 | remainder ( 234 ) | ||||||
| 270 | : | 234 | = | 1 | remainder ( 36 ) | ||||||
| 234 | : | 36 | = | 6 | remainder ( 18 ) | ||||||
| 36 | : | 18 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 18 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.