Find Greatest Common Divisor of 645 and 363, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 645 $ by $ 363 $ and get the remainder
The remainder is positive ($ 282 > 0 $), so we will continue with division.
Step 2 :
Divide $ 363 $ by $ \color{blue}{ 282 } $ and get the remainder
The remainder is still positive ($ 81 > 0 $), so we will continue with division.
Step 3 :
Divide $ 282 $ by $ \color{blue}{ 81 } $ and get the remainder
The remainder is still positive ($ 39 > 0 $), so we will continue with division.
Step 4 :
Divide $ 81 $ by $ \color{blue}{ 39 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 39 $ 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.
| 645 | : | 363 | = | 1 | remainder ( 282 ) | ||||||||
| 363 | : | 282 | = | 1 | remainder ( 81 ) | ||||||||
| 282 | : | 81 | = | 3 | remainder ( 39 ) | ||||||||
| 81 | : | 39 | = | 2 | remainder ( 3 ) | ||||||||
| 39 | : | 3 | = | 13 | remainder ( 0 ) | ||||||||
| GCD = 3 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.