Find Greatest Common Divisor of 1386 and 1170, using Euclidean algorithm.
Answer
The GCD of given numbers is 18.
Explanation
Step 1 :
Divide $ 1386 $ by $ 1170 $ and get the remainder
The remainder is positive ($ 216 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1170 $ by $ \color{blue}{ 216 } $ and get the remainder
The remainder is still positive ($ 90 > 0 $), so we will continue with division.
Step 3 :
Divide $ 216 $ by $ \color{blue}{ 90 } $ and get the remainder
The remainder is still positive ($ 36 > 0 $), so we will continue with division.
Step 4 :
Divide $ 90 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is still positive ($ 18 > 0 $), so we will continue with division.
Step 5 :
Divide $ 36 $ by $ \color{blue}{ 18 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 18 }} $.
We can summarize an algorithm into a following table.
| 1386 | : | 1170 | = | 1 | remainder ( 216 ) | ||||||||
| 1170 | : | 216 | = | 5 | remainder ( 90 ) | ||||||||
| 216 | : | 90 | = | 2 | remainder ( 36 ) | ||||||||
| 90 | : | 36 | = | 2 | remainder ( 18 ) | ||||||||
| 36 | : | 18 | = | 2 | remainder ( 0 ) | ||||||||
| GCD = 18 | |||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.