Find Greatest Common Divisor of 662 and 404, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 662 $ by $ 404 $ and get the remainder
The remainder is positive ($ 258 > 0 $), so we will continue with division.
Step 2 :
Divide $ 404 $ by $ \color{blue}{ 258 } $ and get the remainder
The remainder is still positive ($ 146 > 0 $), so we will continue with division.
Step 3 :
Divide $ 258 $ by $ \color{blue}{ 146 } $ and get the remainder
The remainder is still positive ($ 112 > 0 $), so we will continue with division.
Step 4 :
Divide $ 146 $ by $ \color{blue}{ 112 } $ and get the remainder
The remainder is still positive ($ 34 > 0 $), so we will continue with division.
Step 5 :
Divide $ 112 $ by $ \color{blue}{ 34 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 6 :
Divide $ 34 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 7 :
Divide $ 10 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 8 :
Divide $ 4 $ 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 | : | 404 | = | 1 | remainder ( 258 ) | ||||||||||||||
| 404 | : | 258 | = | 1 | remainder ( 146 ) | ||||||||||||||
| 258 | : | 146 | = | 1 | remainder ( 112 ) | ||||||||||||||
| 146 | : | 112 | = | 1 | remainder ( 34 ) | ||||||||||||||
| 112 | : | 34 | = | 3 | remainder ( 10 ) | ||||||||||||||
| 34 | : | 10 | = | 3 | remainder ( 4 ) | ||||||||||||||
| 10 | : | 4 | = | 2 | remainder ( 2 ) | ||||||||||||||
| 4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||||||||||
| GCD = 2 | |||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.