Find Greatest Common Divisor of 132 and 318, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 318 $ by $ 132 $ and get the remainder
The remainder is positive ($ 54 > 0 $), so we will continue with division.
Step 2 :
Divide $ 132 $ by $ \color{blue}{ 54 } $ and get the remainder
The remainder is still positive ($ 24 > 0 $), so we will continue with division.
Step 3 :
Divide $ 54 $ by $ \color{blue}{ 24 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 24 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 6 }} $.
We can summarize an algorithm into a following table.
| 318 | : | 132 | = | 2 | remainder ( 54 ) | ||||||
| 132 | : | 54 | = | 2 | remainder ( 24 ) | ||||||
| 54 | : | 24 | = | 2 | remainder ( 6 ) | ||||||
| 24 | : | 6 | = | 4 | remainder ( 0 ) | ||||||
| GCD = 6 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.