Find Greatest Common Divisor of 58 and 32, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 58 $ by $ 32 $ and get the remainder
The remainder is positive ($ 26 > 0 $), so we will continue with division.
Step 2 :
Divide $ 32 $ by $ \color{blue}{ 26 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 3 :
Divide $ 26 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 4 :
Divide $ 6 $ 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 | : | 32 | = | 1 | remainder ( 26 ) | ||||||
| 32 | : | 26 | = | 1 | remainder ( 6 ) | ||||||
| 26 | : | 6 | = | 4 | remainder ( 2 ) | ||||||
| 6 | : | 2 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 2 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.