Find Greatest Common Divisor of 504 and 385, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 :
Divide $ 504 $ by $ 385 $ and get the remainder
The remainder is positive ($ 119 > 0 $), so we will continue with division.
Step 2 :
Divide $ 385 $ by $ \color{blue}{ 119 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 3 :
Divide $ 119 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 4 :
Divide $ 28 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
| 504 | : | 385 | = | 1 | remainder ( 119 ) | ||||||
| 385 | : | 119 | = | 3 | remainder ( 28 ) | ||||||
| 119 | : | 28 | = | 4 | remainder ( 7 ) | ||||||
| 28 | : | 7 | = | 4 | remainder ( 0 ) | ||||||
| GCD = 7 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.