Find Greatest Common Divisor of 2016 and 217, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 :
Divide $ 2016 $ by $ 217 $ and get the remainder
The remainder is positive ($ 63 > 0 $), so we will continue with division.
Step 2 :
Divide $ 217 $ by $ \color{blue}{ 63 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 3 :
Divide $ 63 $ 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.
| 2016 | : | 217 | = | 9 | remainder ( 63 ) | ||||||
| 217 | : | 63 | = | 3 | remainder ( 28 ) | ||||||
| 63 | : | 28 | = | 2 | 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.