Find Greatest Common Divisor of 414 and 662, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 662 $ by $ 414 $ and get the remainder
The remainder is positive ($ 248 > 0 $), so we will continue with division.
Step 2 :
Divide $ 414 $ by $ \color{blue}{ 248 } $ and get the remainder
The remainder is still positive ($ 166 > 0 $), so we will continue with division.
Step 3 :
Divide $ 248 $ by $ \color{blue}{ 166 } $ and get the remainder
The remainder is still positive ($ 82 > 0 $), so we will continue with division.
Step 4 :
Divide $ 166 $ by $ \color{blue}{ 82 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 82 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
| 662 | : | 414 | = | 1 | remainder ( 248 ) | ||||||||
| 414 | : | 248 | = | 1 | remainder ( 166 ) | ||||||||
| 248 | : | 166 | = | 1 | remainder ( 82 ) | ||||||||
| 166 | : | 82 | = | 2 | remainder ( 2 ) | ||||||||
| 82 | : | 2 | = | 41 | remainder ( 0 ) | ||||||||
| GCD = 2 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.