Find Greatest Common Divisor of 316 and 180, using Euclidean algorithm.
Answer
The GCD of given numbers is 4.
Explanation
Step 1 :
Divide $ 316 $ by $ 180 $ and get the remainder
The remainder is positive ($ 136 > 0 $), so we will continue with division.
Step 2 :
Divide $ 180 $ by $ \color{blue}{ 136 } $ and get the remainder
The remainder is still positive ($ 44 > 0 $), so we will continue with division.
Step 3 :
Divide $ 136 $ by $ \color{blue}{ 44 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
Divide $ 44 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 4 }} $.
We can summarize an algorithm into a following table.
| 316 | : | 180 | = | 1 | remainder ( 136 ) | ||||||
| 180 | : | 136 | = | 1 | remainder ( 44 ) | ||||||
| 136 | : | 44 | = | 3 | remainder ( 4 ) | ||||||
| 44 | : | 4 | = | 11 | remainder ( 0 ) | ||||||
| GCD = 4 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.