Find Greatest Common Divisor of 483 and 360, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 483 $ by $ 360 $ and get the remainder
The remainder is positive ($ 123 > 0 $), so we will continue with division.
Step 2 :
Divide $ 360 $ by $ \color{blue}{ 123 } $ and get the remainder
The remainder is still positive ($ 114 > 0 $), so we will continue with division.
Step 3 :
Divide $ 123 $ by $ \color{blue}{ 114 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 4 :
Divide $ 114 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 5 :
Divide $ 9 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 6 :
Divide $ 6 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 483 | : | 360 | = | 1 | remainder ( 123 ) | ||||||||||
| 360 | : | 123 | = | 2 | remainder ( 114 ) | ||||||||||
| 123 | : | 114 | = | 1 | remainder ( 9 ) | ||||||||||
| 114 | : | 9 | = | 12 | remainder ( 6 ) | ||||||||||
| 9 | : | 6 | = | 1 | remainder ( 3 ) | ||||||||||
| 6 | : | 3 | = | 2 | remainder ( 0 ) | ||||||||||
| GCD = 3 | |||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.