Find Greatest Common Divisor of 2561124 and 46064, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 2561124 $ by $ 46064 $ and get the remainder
The remainder is positive ($ 27604 > 0 $), so we will continue with division.
Step 2 :
Divide $ 46064 $ by $ \color{blue}{ 27604 } $ and get the remainder
The remainder is still positive ($ 18460 > 0 $), so we will continue with division.
Step 3 :
Divide $ 27604 $ by $ \color{blue}{ 18460 } $ and get the remainder
The remainder is still positive ($ 9144 > 0 $), so we will continue with division.
Step 4 :
Divide $ 18460 $ by $ \color{blue}{ 9144 } $ and get the remainder
The remainder is still positive ($ 172 > 0 $), so we will continue with division.
Step 5 :
Divide $ 9144 $ by $ \color{blue}{ 172 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 6 :
Divide $ 172 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 7 :
Divide $ 28 $ 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.
| 2561124 | : | 46064 | = | 55 | remainder ( 27604 ) | ||||||||||||
| 46064 | : | 27604 | = | 1 | remainder ( 18460 ) | ||||||||||||
| 27604 | : | 18460 | = | 1 | remainder ( 9144 ) | ||||||||||||
| 18460 | : | 9144 | = | 2 | remainder ( 172 ) | ||||||||||||
| 9144 | : | 172 | = | 53 | remainder ( 28 ) | ||||||||||||
| 172 | : | 28 | = | 6 | remainder ( 4 ) | ||||||||||||
| 28 | : | 4 | = | 7 | remainder ( 0 ) | ||||||||||||
| GCD = 4 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.