Find Greatest Common Divisor of 4453 and 5767, using Euclidean algorithm.
Answer
The GCD of given numbers is 73.
Explanation
Step 1 :
Divide $ 5767 $ by $ 4453 $ and get the remainder
The remainder is positive ($ 1314 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4453 $ by $ \color{blue}{ 1314 } $ and get the remainder
The remainder is still positive ($ 511 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1314 $ by $ \color{blue}{ 511 } $ and get the remainder
The remainder is still positive ($ 292 > 0 $), so we will continue with division.
Step 4 :
Divide $ 511 $ by $ \color{blue}{ 292 } $ and get the remainder
The remainder is still positive ($ 219 > 0 $), so we will continue with division.
Step 5 :
Divide $ 292 $ by $ \color{blue}{ 219 } $ and get the remainder
The remainder is still positive ($ 73 > 0 $), so we will continue with division.
Step 6 :
Divide $ 219 $ by $ \color{blue}{ 73 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 73 }} $.
We can summarize an algorithm into a following table.
| 5767 | : | 4453 | = | 1 | remainder ( 1314 ) | ||||||||||
| 4453 | : | 1314 | = | 3 | remainder ( 511 ) | ||||||||||
| 1314 | : | 511 | = | 2 | remainder ( 292 ) | ||||||||||
| 511 | : | 292 | = | 1 | remainder ( 219 ) | ||||||||||
| 292 | : | 219 | = | 1 | remainder ( 73 ) | ||||||||||
| 219 | : | 73 | = | 3 | remainder ( 0 ) | ||||||||||
| GCD = 73 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.