Find Greatest Common Divisor of 3289 and 2415, using Euclidean algorithm.
Answer
The GCD of given numbers is 23.
Explanation
Step 1 :
Divide $ 3289 $ by $ 2415 $ and get the remainder
The remainder is positive ($ 874 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2415 $ by $ \color{blue}{ 874 } $ and get the remainder
The remainder is still positive ($ 667 > 0 $), so we will continue with division.
Step 3 :
Divide $ 874 $ by $ \color{blue}{ 667 } $ and get the remainder
The remainder is still positive ($ 207 > 0 $), so we will continue with division.
Step 4 :
Divide $ 667 $ by $ \color{blue}{ 207 } $ and get the remainder
The remainder is still positive ($ 46 > 0 $), so we will continue with division.
Step 5 :
Divide $ 207 $ by $ \color{blue}{ 46 } $ and get the remainder
The remainder is still positive ($ 23 > 0 $), so we will continue with division.
Step 6 :
Divide $ 46 $ by $ \color{blue}{ 23 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 23 }} $.
We can summarize an algorithm into a following table.
| 3289 | : | 2415 | = | 1 | remainder ( 874 ) | ||||||||||
| 2415 | : | 874 | = | 2 | remainder ( 667 ) | ||||||||||
| 874 | : | 667 | = | 1 | remainder ( 207 ) | ||||||||||
| 667 | : | 207 | = | 3 | remainder ( 46 ) | ||||||||||
| 207 | : | 46 | = | 4 | remainder ( 23 ) | ||||||||||
| 46 | : | 23 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 23 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.