Find Greatest Common Divisor of 634 and 472, using Euclidean algorithm.
Answer
The GCD of given numbers is 2.
Explanation
Step 1 :
Divide $ 634 $ by $ 472 $ and get the remainder
The remainder is positive ($ 162 > 0 $), so we will continue with division.
Step 2 :
Divide $ 472 $ by $ \color{blue}{ 162 } $ and get the remainder
The remainder is still positive ($ 148 > 0 $), so we will continue with division.
Step 3 :
Divide $ 162 $ by $ \color{blue}{ 148 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 4 :
Divide $ 148 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 14 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 7 :
Divide $ 6 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 2 }} $.
We can summarize an algorithm into a following table.
| 634 | : | 472 | = | 1 | remainder ( 162 ) | ||||||||||||
| 472 | : | 162 | = | 2 | remainder ( 148 ) | ||||||||||||
| 162 | : | 148 | = | 1 | remainder ( 14 ) | ||||||||||||
| 148 | : | 14 | = | 10 | remainder ( 8 ) | ||||||||||||
| 14 | : | 8 | = | 1 | remainder ( 6 ) | ||||||||||||
| 8 | : | 6 | = | 1 | remainder ( 2 ) | ||||||||||||
| 6 | : | 2 | = | 3 | remainder ( 0 ) | ||||||||||||
| GCD = 2 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.