Find Greatest Common Divisor of 300 and 110, using Euclidean algorithm.
Answer
The GCD of given numbers is 10.
Explanation
Step 1 :
Divide $ 300 $ by $ 110 $ and get the remainder
The remainder is positive ($ 80 > 0 $), so we will continue with division.
Step 2 :
Divide $ 110 $ by $ \color{blue}{ 80 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 3 :
Divide $ 80 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 4 :
Divide $ 30 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 5 :
Divide $ 20 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 10 }} $.
We can summarize an algorithm into a following table.
| 300 | : | 110 | = | 2 | remainder ( 80 ) | ||||||||
| 110 | : | 80 | = | 1 | remainder ( 30 ) | ||||||||
| 80 | : | 30 | = | 2 | remainder ( 20 ) | ||||||||
| 30 | : | 20 | = | 1 | remainder ( 10 ) | ||||||||
| 20 | : | 10 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 10 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.