Find Greatest Common Divisor of 44838 and 4830, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 44838 $ by $ 4830 $ and get the remainder
The remainder is positive ($ 1368 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4830 $ by $ \color{blue}{ 1368 } $ and get the remainder
The remainder is still positive ($ 726 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1368 $ by $ \color{blue}{ 726 } $ and get the remainder
The remainder is still positive ($ 642 > 0 $), so we will continue with division.
Step 4 :
Divide $ 726 $ by $ \color{blue}{ 642 } $ and get the remainder
The remainder is still positive ($ 84 > 0 $), so we will continue with division.
Step 5 :
Divide $ 642 $ by $ \color{blue}{ 84 } $ and get the remainder
The remainder is still positive ($ 54 > 0 $), so we will continue with division.
Step 6 :
Divide $ 84 $ by $ \color{blue}{ 54 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 7 :
Divide $ 54 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 8 :
Divide $ 30 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 9 :
Divide $ 24 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
| 44838 | : | 4830 | = | 9 | remainder ( 1368 ) | ||||||||||||||||
| 4830 | : | 1368 | = | 3 | remainder ( 726 ) | ||||||||||||||||
| 1368 | : | 726 | = | 1 | remainder ( 642 ) | ||||||||||||||||
| 726 | : | 642 | = | 1 | remainder ( 84 ) | ||||||||||||||||
| 642 | : | 84 | = | 7 | remainder ( 54 ) | ||||||||||||||||
| 84 | : | 54 | = | 1 | remainder ( 30 ) | ||||||||||||||||
| 54 | : | 30 | = | 1 | remainder ( 24 ) | ||||||||||||||||
| 30 | : | 24 | = | 1 | remainder ( 6 ) | ||||||||||||||||
| 24 | : | 6 | = | 4 | remainder ( 0 ) | ||||||||||||||||
| GCD = 6 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.