Find Greatest Common Divisor of 593 and 1957, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1957 $ by $ 593 $ and get the remainder
The remainder is positive ($ 178 > 0 $), so we will continue with division.
Step 2 :
Divide $ 593 $ by $ \color{blue}{ 178 } $ and get the remainder
The remainder is still positive ($ 59 > 0 $), so we will continue with division.
Step 3 :
Divide $ 178 $ by $ \color{blue}{ 59 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 59 $ 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.
| 1957 | : | 593 | = | 3 | remainder ( 178 ) | ||||||
| 593 | : | 178 | = | 3 | remainder ( 59 ) | ||||||
| 178 | : | 59 | = | 3 | remainder ( 1 ) | ||||||
| 59 | : | 1 | = | 59 | remainder ( 0 ) | ||||||
| GCD = 1 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.