Find Greatest Common Divisor of 466 and 267, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 466 $ by $ 267 $ and get the remainder
The remainder is positive ($ 199 > 0 $), so we will continue with division.
Step 2 :
Divide $ 267 $ by $ \color{blue}{ 199 } $ and get the remainder
The remainder is still positive ($ 68 > 0 $), so we will continue with division.
Step 3 :
Divide $ 199 $ by $ \color{blue}{ 68 } $ and get the remainder
The remainder is still positive ($ 63 > 0 $), so we will continue with division.
Step 4 :
Divide $ 68 $ by $ \color{blue}{ 63 } $ and get the remainder
The remainder is still positive ($ 5 > 0 $), so we will continue with division.
Step 5 :
Divide $ 63 $ by $ \color{blue}{ 5 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 6 :
Divide $ 5 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 8 :
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.
| 466 | : | 267 | = | 1 | remainder ( 199 ) | ||||||||||||||
| 267 | : | 199 | = | 1 | remainder ( 68 ) | ||||||||||||||
| 199 | : | 68 | = | 2 | remainder ( 63 ) | ||||||||||||||
| 68 | : | 63 | = | 1 | remainder ( 5 ) | ||||||||||||||
| 63 | : | 5 | = | 12 | remainder ( 3 ) | ||||||||||||||
| 5 | : | 3 | = | 1 | remainder ( 2 ) | ||||||||||||||
| 3 | : | 2 | = | 1 | 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.