Find Greatest Common Divisor of 12327 and 2409, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 12327 $ by $ 2409 $ and get the remainder
The remainder is positive ($ 282 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2409 $ by $ \color{blue}{ 282 } $ and get the remainder
The remainder is still positive ($ 153 > 0 $), so we will continue with division.
Step 3 :
Divide $ 282 $ by $ \color{blue}{ 153 } $ and get the remainder
The remainder is still positive ($ 129 > 0 $), so we will continue with division.
Step 4 :
Divide $ 153 $ by $ \color{blue}{ 129 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 5 :
Divide $ 129 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 6 :
Divide $ 24 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 7 :
Divide $ 9 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 8 :
Divide $ 6 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 12327 | : | 2409 | = | 5 | remainder ( 282 ) | ||||||||||||||
| 2409 | : | 282 | = | 8 | remainder ( 153 ) | ||||||||||||||
| 282 | : | 153 | = | 1 | remainder ( 129 ) | ||||||||||||||
| 153 | : | 129 | = | 1 | remainder ( 24 ) | ||||||||||||||
| 129 | : | 24 | = | 5 | remainder ( 9 ) | ||||||||||||||
| 24 | : | 9 | = | 2 | remainder ( 6 ) | ||||||||||||||
| 9 | : | 6 | = | 1 | remainder ( 3 ) | ||||||||||||||
| 6 | : | 3 | = | 2 | remainder ( 0 ) | ||||||||||||||
| GCD = 3 | |||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.