Find Greatest Common Divisor of 471 and 9231, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 9231 $ by $ 471 $ and get the remainder
The remainder is positive ($ 282 > 0 $), so we will continue with division.
Step 2 :
Divide $ 471 $ by $ \color{blue}{ 282 } $ and get the remainder
The remainder is still positive ($ 189 > 0 $), so we will continue with division.
Step 3 :
Divide $ 282 $ by $ \color{blue}{ 189 } $ and get the remainder
The remainder is still positive ($ 93 > 0 $), so we will continue with division.
Step 4 :
Divide $ 189 $ by $ \color{blue}{ 93 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 93 $ 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.
| 9231 | : | 471 | = | 19 | remainder ( 282 ) | ||||||||
| 471 | : | 282 | = | 1 | remainder ( 189 ) | ||||||||
| 282 | : | 189 | = | 1 | remainder ( 93 ) | ||||||||
| 189 | : | 93 | = | 2 | remainder ( 3 ) | ||||||||
| 93 | : | 3 | = | 31 | remainder ( 0 ) | ||||||||
| GCD = 3 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.