Find Greatest Common Divisor of 58 and 40, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 58 $ by $ 40 $ and get the remainder
The remainder is positive ($ 18 > 0 $), so we will continue with division.
Step 2 :
Divide $ 40 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 3 :
Divide $ 18 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 4 :
Divide $ 4 $ 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.
| 58 | : | 40 | = | 1 | remainder ( 18 ) | ||||||
| 40 | : | 18 | = | 2 | remainder ( 4 ) | ||||||
| 18 | : | 4 | = | 4 | remainder ( 2 ) | ||||||
| 4 | : | 2 | = | 2 | remainder ( 0 ) | ||||||
| GCD = 2 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.