Find Greatest Common Divisor of 3768 and 1701, using Euclidean algorithm.
Answer
The GCD of given numbers is 3.
Explanation
Step 1 :
Divide $ 3768 $ by $ 1701 $ and get the remainder
The remainder is positive ($ 366 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1701 $ by $ \color{blue}{ 366 } $ and get the remainder
The remainder is still positive ($ 237 > 0 $), so we will continue with division.
Step 3 :
Divide $ 366 $ by $ \color{blue}{ 237 } $ and get the remainder
The remainder is still positive ($ 129 > 0 $), so we will continue with division.
Step 4 :
Divide $ 237 $ by $ \color{blue}{ 129 } $ and get the remainder
The remainder is still positive ($ 108 > 0 $), so we will continue with division.
Step 5 :
Divide $ 129 $ by $ \color{blue}{ 108 } $ and get the remainder
The remainder is still positive ($ 21 > 0 $), so we will continue with division.
Step 6 :
Divide $ 108 $ by $ \color{blue}{ 21 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 7 :
Divide $ 21 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
| 3768 | : | 1701 | = | 2 | remainder ( 366 ) | ||||||||||||
| 1701 | : | 366 | = | 4 | remainder ( 237 ) | ||||||||||||
| 366 | : | 237 | = | 1 | remainder ( 129 ) | ||||||||||||
| 237 | : | 129 | = | 1 | remainder ( 108 ) | ||||||||||||
| 129 | : | 108 | = | 1 | remainder ( 21 ) | ||||||||||||
| 108 | : | 21 | = | 5 | remainder ( 3 ) | ||||||||||||
| 21 | : | 3 | = | 7 | remainder ( 0 ) | ||||||||||||
| GCD = 3 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.