Find Greatest Common Divisor of 1372 and 5733, using Euclidean algorithm.
Answer
The GCD of given numbers is 49.
Explanation
Step 1 :
Divide $ 5733 $ by $ 1372 $ and get the remainder
The remainder is positive ($ 245 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1372 $ by $ \color{blue}{ 245 } $ and get the remainder
The remainder is still positive ($ 147 > 0 $), so we will continue with division.
Step 3 :
Divide $ 245 $ by $ \color{blue}{ 147 } $ and get the remainder
The remainder is still positive ($ 98 > 0 $), so we will continue with division.
Step 4 :
Divide $ 147 $ by $ \color{blue}{ 98 } $ and get the remainder
The remainder is still positive ($ 49 > 0 $), so we will continue with division.
Step 5 :
Divide $ 98 $ by $ \color{blue}{ 49 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 49 }} $.
We can summarize an algorithm into a following table.
| 5733 | : | 1372 | = | 4 | remainder ( 245 ) | ||||||||
| 1372 | : | 245 | = | 5 | remainder ( 147 ) | ||||||||
| 245 | : | 147 | = | 1 | remainder ( 98 ) | ||||||||
| 147 | : | 98 | = | 1 | remainder ( 49 ) | ||||||||
| 98 | : | 49 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 49 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.