Find Greatest Common Divisor of 1492 and 1066, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 1492 $ by $ 1066 $ and get the remainder
The remainder is positive ($ 426 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1066 $ by $ \color{blue}{ 426 } $ and get the remainder
The remainder is still positive ($ 214 > 0 $), so we will continue with division.
Step 3 :
Divide $ 426 $ by $ \color{blue}{ 214 } $ and get the remainder
The remainder is still positive ($ 212 > 0 $), so we will continue with division.
Step 4 :
Divide $ 214 $ by $ \color{blue}{ 212 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 5 :
Divide $ 212 $ 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.
| 1492 | : | 1066 | = | 1 | remainder ( 426 ) | ||||||||
| 1066 | : | 426 | = | 2 | remainder ( 214 ) | ||||||||
| 426 | : | 214 | = | 1 | remainder ( 212 ) | ||||||||
| 214 | : | 212 | = | 1 | remainder ( 2 ) | ||||||||
| 212 | : | 2 | = | 106 | remainder ( 0 ) | ||||||||
| GCD = 2 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.