Find Greatest Common Divisor of 3367 and 3219, using Euclidean algorithm.
Answer
The GCD of given numbers is 37.
Explanation
Step 1 :
Divide $ 3367 $ by $ 3219 $ and get the remainder
The remainder is positive ($ 148 > 0 $), so we will continue with division.
Step 2 :
Divide $ 3219 $ by $ \color{blue}{ 148 } $ and get the remainder
The remainder is still positive ($ 111 > 0 $), so we will continue with division.
Step 3 :
Divide $ 148 $ by $ \color{blue}{ 111 } $ and get the remainder
The remainder is still positive ($ 37 > 0 $), so we will continue with division.
Step 4 :
Divide $ 111 $ by $ \color{blue}{ 37 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 37 }} $.
We can summarize an algorithm into a following table.
| 3367 | : | 3219 | = | 1 | remainder ( 148 ) | ||||||
| 3219 | : | 148 | = | 21 | remainder ( 111 ) | ||||||
| 148 | : | 111 | = | 1 | remainder ( 37 ) | ||||||
| 111 | : | 37 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 37 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.