Find Greatest Common Divisor of 28844 and 15712, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 28844 $ by $ 15712 $ and get the remainder
The remainder is positive ($ 13132 > 0 $), so we will continue with division.
Step 2 :
Divide $ 15712 $ by $ \color{blue}{ 13132 } $ and get the remainder
The remainder is still positive ($ 2580 > 0 $), so we will continue with division.
Step 3 :
Divide $ 13132 $ by $ \color{blue}{ 2580 } $ and get the remainder
The remainder is still positive ($ 232 > 0 $), so we will continue with division.
Step 4 :
Divide $ 2580 $ by $ \color{blue}{ 232 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 5 :
Divide $ 232 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 6 :
Divide $ 28 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 7 :
Divide $ 8 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 28844 | : | 15712 | = | 1 | remainder ( 13132 ) | ||||||||||||
| 15712 | : | 13132 | = | 1 | remainder ( 2580 ) | ||||||||||||
| 13132 | : | 2580 | = | 5 | remainder ( 232 ) | ||||||||||||
| 2580 | : | 232 | = | 11 | remainder ( 28 ) | ||||||||||||
| 232 | : | 28 | = | 8 | remainder ( 8 ) | ||||||||||||
| 28 | : | 8 | = | 3 | remainder ( 4 ) | ||||||||||||
| 8 | : | 4 | = | 2 | remainder ( 0 ) | ||||||||||||
| GCD = 4 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.