Find Greatest Common Divisor of 378 and 140, using Euclidean algorithm.
Answer
The GCD of given numbers is 14.
Explanation
Step 1 :
Divide $ 378 $ by $ 140 $ and get the remainder
The remainder is positive ($ 98 > 0 $), so we will continue with division.
Step 2 :
Divide $ 140 $ by $ \color{blue}{ 98 } $ and get the remainder
The remainder is still positive ($ 42 > 0 $), so we will continue with division.
Step 3 :
Divide $ 98 $ by $ \color{blue}{ 42 } $ and get the remainder
The remainder is still positive ($ 14 > 0 $), so we will continue with division.
Step 4 :
Divide $ 42 $ by $ \color{blue}{ 14 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 14 }} $.
We can summarize an algorithm into a following table.
| 378 | : | 140 | = | 2 | remainder ( 98 ) | ||||||
| 140 | : | 98 | = | 1 | remainder ( 42 ) | ||||||
| 98 | : | 42 | = | 2 | remainder ( 14 ) | ||||||
| 42 | : | 14 | = | 3 | remainder ( 0 ) | ||||||
| GCD = 14 | |||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.