Find Greatest Common Divisor of 62 and 83, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 83 $ by $ 62 $ and get the remainder
The remainder is positive ($ 21 > 0 $), so we will continue with division.
Step 2 :
Divide $ 62 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 20 > 0 $), so we will continue with division.
Step 3 :
Divide $ 21 $ by $ \color{blue}{ 20 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 20 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 83 | : | 62 | = | 1 | remainder ( 21 ) | ||||||
| 62 | : | 21 | = | 2 | remainder ( 20 ) | ||||||
| 21 | : | 20 | = | 1 | remainder ( 1 ) | ||||||
| 20 | : | 1 | = | 20 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.