Find Greatest Common Divisor of 216 and 68, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 216 $ by $ 68 $ and get the remainder
The remainder is positive ($ 12 > 0 $), so we will continue with division.
Step 2 :
Divide $ 68 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 3 :
Divide $ 12 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 216 | : | 68 | = | 3 | remainder ( 12 ) | ||||||
| 68 | : | 12 | = | 5 | remainder ( 8 ) | ||||||
| 12 | : | 8 | = | 1 | remainder ( 4 ) | ||||||
| 8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 4 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.