Find Greatest Common Divisor of 1739 and 9923, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 9923 $ by $ 1739 $ and get the remainder
The remainder is positive ($ 1228 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1739 $ by $ \color{blue}{ 1228 } $ and get the remainder
The remainder is still positive ($ 511 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1228 $ by $ \color{blue}{ 511 } $ and get the remainder
The remainder is still positive ($ 206 > 0 $), so we will continue with division.
Step 4 :
Divide $ 511 $ by $ \color{blue}{ 206 } $ and get the remainder
The remainder is still positive ($ 99 > 0 $), so we will continue with division.
Step 5 :
Divide $ 206 $ by $ \color{blue}{ 99 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 6 :
Divide $ 99 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 7 :
Divide $ 8 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 8 :
Divide $ 3 $ by $ \color{blue}{ 2 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 9 :
Divide $ 2 $ by $ \color{blue}{ 1 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 1 }} $.
We can summarize an algorithm into a following table.
| 9923 | : | 1739 | = | 5 | remainder ( 1228 ) | ||||||||||||||||
| 1739 | : | 1228 | = | 1 | remainder ( 511 ) | ||||||||||||||||
| 1228 | : | 511 | = | 2 | remainder ( 206 ) | ||||||||||||||||
| 511 | : | 206 | = | 2 | remainder ( 99 ) | ||||||||||||||||
| 206 | : | 99 | = | 2 | remainder ( 8 ) | ||||||||||||||||
| 99 | : | 8 | = | 12 | remainder ( 3 ) | ||||||||||||||||
| 8 | : | 3 | = | 2 | remainder ( 2 ) | ||||||||||||||||
| 3 | : | 2 | = | 1 | remainder ( 1 ) | ||||||||||||||||
| 2 | : | 1 | = | 2 | remainder ( 0 ) | ||||||||||||||||
| GCD = 1 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.