Find Greatest Common Divisor of 43650 and 4980, using Euclidean algorithm.
Answer
The GCD of given numbers is 30.
Explanation
Step 1 :
Divide $ 43650 $ by $ 4980 $ and get the remainder
The remainder is positive ($ 3810 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4980 $ by $ \color{blue}{ 3810 } $ and get the remainder
The remainder is still positive ($ 1170 > 0 $), so we will continue with division.
Step 3 :
Divide $ 3810 $ by $ \color{blue}{ 1170 } $ and get the remainder
The remainder is still positive ($ 300 > 0 $), so we will continue with division.
Step 4 :
Divide $ 1170 $ by $ \color{blue}{ 300 } $ and get the remainder
The remainder is still positive ($ 270 > 0 $), so we will continue with division.
Step 5 :
Divide $ 300 $ by $ \color{blue}{ 270 } $ and get the remainder
The remainder is still positive ($ 30 > 0 $), so we will continue with division.
Step 6 :
Divide $ 270 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 30 }} $.
We can summarize an algorithm into a following table.
| 43650 | : | 4980 | = | 8 | remainder ( 3810 ) | ||||||||||
| 4980 | : | 3810 | = | 1 | remainder ( 1170 ) | ||||||||||
| 3810 | : | 1170 | = | 3 | remainder ( 300 ) | ||||||||||
| 1170 | : | 300 | = | 3 | remainder ( 270 ) | ||||||||||
| 300 | : | 270 | = | 1 | remainder ( 30 ) | ||||||||||
| 270 | : | 30 | = | 9 | remainder ( 0 ) | ||||||||||
| GCD = 30 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.