Find Greatest Common Divisor of 710 and 310, using Euclidean algorithm.
Answer
The GCD of given numbers is 10.
Explanation
Step 1 :
Divide $ 710 $ by $ 310 $ and get the remainder
The remainder is positive ($ 90 > 0 $), so we will continue with division.
Step 2 :
Divide $ 310 $ by $ \color{blue}{ 90 } $ and get the remainder
The remainder is still positive ($ 40 > 0 $), so we will continue with division.
Step 3 :
Divide $ 90 $ by $ \color{blue}{ 40 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 4 :
Divide $ 40 $ 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.
| 710 | : | 310 | = | 2 | remainder ( 90 ) | ||||||
| 310 | : | 90 | = | 3 | remainder ( 40 ) | ||||||
| 90 | : | 40 | = | 2 | remainder ( 10 ) | ||||||
| 40 | : | 10 | = | 4 | remainder ( 0 ) | ||||||
| GCD = 10 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.