Find Greatest Common Divisor of 196 and 262, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 262 $ by $ 196 $ and get the remainder
The remainder is positive ($ 66 > 0 $), so we will continue with division.
Step 2 :
Divide $ 196 $ by $ \color{blue}{ 66 } $ and get the remainder
The remainder is still positive ($ 64 > 0 $), so we will continue with division.
Step 3 :
Divide $ 66 $ by $ \color{blue}{ 64 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 4 :
Divide $ 64 $ 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.
| 262 | : | 196 | = | 1 | remainder ( 66 ) | ||||||
| 196 | : | 66 | = | 2 | remainder ( 64 ) | ||||||
| 66 | : | 64 | = | 1 | remainder ( 2 ) | ||||||
| 64 | : | 2 | = | 32 | remainder ( 0 ) | ||||||
| GCD = 2 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.