Find Greatest Common Divisor of 12728 and 20000, using Euclidean algorithm.
Answer
The GCD of given numbers is 8.
Explanation
Step 1 :
Divide $ 20000 $ by $ 12728 $ and get the remainder
The remainder is positive ($ 7272 > 0 $), so we will continue with division.
Step 2 :
Divide $ 12728 $ by $ \color{blue}{ 7272 } $ and get the remainder
The remainder is still positive ($ 5456 > 0 $), so we will continue with division.
Step 3 :
Divide $ 7272 $ by $ \color{blue}{ 5456 } $ and get the remainder
The remainder is still positive ($ 1816 > 0 $), so we will continue with division.
Step 4 :
Divide $ 5456 $ by $ \color{blue}{ 1816 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 1816 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 8 }} $.
We can summarize an algorithm into a following table.
| 20000 | : | 12728 | = | 1 | remainder ( 7272 ) | ||||||||
| 12728 | : | 7272 | = | 1 | remainder ( 5456 ) | ||||||||
| 7272 | : | 5456 | = | 1 | remainder ( 1816 ) | ||||||||
| 5456 | : | 1816 | = | 3 | remainder ( 8 ) | ||||||||
| 1816 | : | 8 | = | 227 | remainder ( 0 ) | ||||||||
| GCD = 8 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.