Find Greatest Common Divisor of 9801 and 1452891650, using Euclidean algorithm.
Answer
The GCD of given numbers is 1.
Explanation
Step 1 :
Divide $ 1452891650 $ by $ 9801 $ and get the remainder
The remainder is positive ($ 1211 > 0 $), so we will continue with division.
Step 2 :
Divide $ 9801 $ by $ \color{blue}{ 1211 } $ and get the remainder
The remainder is still positive ($ 113 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1211 $ by $ \color{blue}{ 113 } $ and get the remainder
The remainder is still positive ($ 81 > 0 $), so we will continue with division.
Step 4 :
Divide $ 113 $ by $ \color{blue}{ 81 } $ and get the remainder
The remainder is still positive ($ 32 > 0 $), so we will continue with division.
Step 5 :
Divide $ 81 $ by $ \color{blue}{ 32 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 6 :
Divide $ 32 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 7 :
Divide $ 17 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 2 > 0 $), so we will continue with division.
Step 8 :
Divide $ 15 $ 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.
| 1452891650 | : | 9801 | = | 148239 | remainder ( 1211 ) | ||||||||||||||||
| 9801 | : | 1211 | = | 8 | remainder ( 113 ) | ||||||||||||||||
| 1211 | : | 113 | = | 10 | remainder ( 81 ) | ||||||||||||||||
| 113 | : | 81 | = | 1 | remainder ( 32 ) | ||||||||||||||||
| 81 | : | 32 | = | 2 | remainder ( 17 ) | ||||||||||||||||
| 32 | : | 17 | = | 1 | remainder ( 15 ) | ||||||||||||||||
| 17 | : | 15 | = | 1 | remainder ( 2 ) | ||||||||||||||||
| 15 | : | 2 | = | 7 | 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.