Find Greatest Common Divisor of 2533 and 466, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 2533 $ by $ 466 $ and get the remainder
The remainder is positive ($ 203 > 0 $), so we will continue with division.
Step 2 :
Divide $ 466 $ by $ \color{blue}{ 203 } $ and get the remainder
The remainder is still positive ($ 60 > 0 $), so we will continue with division.
Step 3 :
Divide $ 203 $ by $ \color{blue}{ 60 } $ and get the remainder
The remainder is still positive ($ 23 > 0 $), so we will continue with division.
Step 4 :
Divide $ 60 $ by $ \color{blue}{ 23 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 5 :
Divide $ 23 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 6 :
Divide $ 14 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 7 :
Divide $ 9 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 8 :
Divide $ 5 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 9 :
Divide $ 4 $ 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.
| 2533 | : | 466 | = | 5 | remainder ( 203 ) | ||||||||||||||||
| 466 | : | 203 | = | 2 | remainder ( 60 ) | ||||||||||||||||
| 203 | : | 60 | = | 3 | remainder ( 23 ) | ||||||||||||||||
| 60 | : | 23 | = | 2 | remainder ( 14 ) | ||||||||||||||||
| 23 | : | 14 | = | 1 | remainder ( 9 ) | ||||||||||||||||
| 14 | : | 9 | = | 1 | remainder ( 5 ) | ||||||||||||||||
| 9 | : | 5 | = | 1 | remainder ( 4 ) | ||||||||||||||||
| 5 | : | 4 | = | 1 | remainder ( 1 ) | ||||||||||||||||
| 4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||||||||||||
| GCD = 1 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.