Find Greatest Common Divisor of 54796 and 605, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 54796 $ by $ 605 $ and get the remainder
The remainder is positive ($ 346 > 0 $), so we will continue with division.
Step 2 :
Divide $ 605 $ by $ \color{blue}{ 346 } $ and get the remainder
The remainder is still positive ($ 259 > 0 $), so we will continue with division.
Step 3 :
Divide $ 346 $ by $ \color{blue}{ 259 } $ and get the remainder
The remainder is still positive ($ 87 > 0 $), so we will continue with division.
Step 4 :
Divide $ 259 $ by $ \color{blue}{ 87 } $ and get the remainder
The remainder is still positive ($ 85 > 0 $), so we will continue with division.
Step 5 :
Divide $ 87 $ by $ \color{blue}{ 85 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 6 :
Divide $ 85 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 7 :
Divide $ 2 $ 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.
| 54796 | : | 605 | = | 90 | remainder ( 346 ) | ||||||||||||
| 605 | : | 346 | = | 1 | remainder ( 259 ) | ||||||||||||
| 346 | : | 259 | = | 1 | remainder ( 87 ) | ||||||||||||
| 259 | : | 87 | = | 2 | remainder ( 85 ) | ||||||||||||
| 87 | : | 85 | = | 1 | remainder ( 2 ) | ||||||||||||
| 85 | : | 2 | = | 42 | remainder ( 1 ) | ||||||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||
| GCD = 1 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.