Find Greatest Common Divisor of 270 and 192, using Euclidean algorithm.
Answer
The GCD of given numbers is 6.
Explanation
Step 1 :
Divide $ 270 $ by $ 192 $ and get the remainder
The remainder is positive ($ 78 > 0 $), so we will continue with division.
Step 2 :
Divide $ 192 $ by $ \color{blue}{ 78 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 3 :
Divide $ 78 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 36 $ 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.
| 270 | : | 192 | = | 1 | remainder ( 78 ) | ||||||
| 192 | : | 78 | = | 2 | remainder ( 36 ) | ||||||
| 78 | : | 36 | = | 2 | remainder ( 6 ) | ||||||
| 36 | : | 6 | = | 6 | remainder ( 0 ) | ||||||
| GCD = 6 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.