Find Greatest Common Divisor of 82 and 70, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 82 $ by $ 70 $ and get the remainder
The remainder is positive ($ 12 > 0 $), so we will continue with division.
Step 2 :
Divide $ 70 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is still positive ($ 10 > 0 $), so we will continue with division.
Step 3 :
Divide $ 12 $ by $ \color{blue}{ 10 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 4 :
Divide $ 10 $ 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.
| 82 | : | 70 | = | 1 | remainder ( 12 ) | ||||||
| 70 | : | 12 | = | 5 | remainder ( 10 ) | ||||||
| 12 | : | 10 | = | 1 | remainder ( 2 ) | ||||||
| 10 | : | 2 | = | 5 | remainder ( 0 ) | ||||||
| GCD = 2 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.