Find Greatest Common Divisor of 2947 and 3997, using Euclidean algorithm.
Answer
The GCD of given numbers is 7.
Explanation
Step 1 :
Divide $ 3997 $ by $ 2947 $ and get the remainder
The remainder is positive ($ 1050 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2947 $ by $ \color{blue}{ 1050 } $ and get the remainder
The remainder is still positive ($ 847 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1050 $ by $ \color{blue}{ 847 } $ and get the remainder
The remainder is still positive ($ 203 > 0 $), so we will continue with division.
Step 4 :
Divide $ 847 $ by $ \color{blue}{ 203 } $ and get the remainder
The remainder is still positive ($ 35 > 0 $), so we will continue with division.
Step 5 :
Divide $ 203 $ by $ \color{blue}{ 35 } $ and get the remainder
The remainder is still positive ($ 28 > 0 $), so we will continue with division.
Step 6 :
Divide $ 35 $ by $ \color{blue}{ 28 } $ and get the remainder
The remainder is still positive ($ 7 > 0 $), so we will continue with division.
Step 7 :
Divide $ 28 $ by $ \color{blue}{ 7 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 7 }} $.
We can summarize an algorithm into a following table.
| 3997 | : | 2947 | = | 1 | remainder ( 1050 ) | ||||||||||||
| 2947 | : | 1050 | = | 2 | remainder ( 847 ) | ||||||||||||
| 1050 | : | 847 | = | 1 | remainder ( 203 ) | ||||||||||||
| 847 | : | 203 | = | 4 | remainder ( 35 ) | ||||||||||||
| 203 | : | 35 | = | 5 | remainder ( 28 ) | ||||||||||||
| 35 | : | 28 | = | 1 | remainder ( 7 ) | ||||||||||||
| 28 | : | 7 | = | 4 | remainder ( 0 ) | ||||||||||||
| GCD = 7 | |||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.