Find Greatest Common Divisor of 17601969 and 2364768, using Euclidean algorithm.
Answer
The GCD of given numbers is 483.
Explanation
Step 1 :
Divide $ 17601969 $ by $ 2364768 $ and get the remainder
The remainder is positive ($ 1048593 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2364768 $ by $ \color{blue}{ 1048593 } $ and get the remainder
The remainder is still positive ($ 267582 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1048593 $ by $ \color{blue}{ 267582 } $ and get the remainder
The remainder is still positive ($ 245847 > 0 $), so we will continue with division.
Step 4 :
Divide $ 267582 $ by $ \color{blue}{ 245847 } $ and get the remainder
The remainder is still positive ($ 21735 > 0 $), so we will continue with division.
Step 5 :
Divide $ 245847 $ by $ \color{blue}{ 21735 } $ and get the remainder
The remainder is still positive ($ 6762 > 0 $), so we will continue with division.
Step 6 :
Divide $ 21735 $ by $ \color{blue}{ 6762 } $ and get the remainder
The remainder is still positive ($ 1449 > 0 $), so we will continue with division.
Step 7 :
Divide $ 6762 $ by $ \color{blue}{ 1449 } $ and get the remainder
The remainder is still positive ($ 966 > 0 $), so we will continue with division.
Step 8 :
Divide $ 1449 $ by $ \color{blue}{ 966 } $ and get the remainder
The remainder is still positive ($ 483 > 0 $), so we will continue with division.
Step 9 :
Divide $ 966 $ by $ \color{blue}{ 483 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 483 }} $.
We can summarize an algorithm into a following table.
| 17601969 | : | 2364768 | = | 7 | remainder ( 1048593 ) | ||||||||||||||||
| 2364768 | : | 1048593 | = | 2 | remainder ( 267582 ) | ||||||||||||||||
| 1048593 | : | 267582 | = | 3 | remainder ( 245847 ) | ||||||||||||||||
| 267582 | : | 245847 | = | 1 | remainder ( 21735 ) | ||||||||||||||||
| 245847 | : | 21735 | = | 11 | remainder ( 6762 ) | ||||||||||||||||
| 21735 | : | 6762 | = | 3 | remainder ( 1449 ) | ||||||||||||||||
| 6762 | : | 1449 | = | 4 | remainder ( 966 ) | ||||||||||||||||
| 1449 | : | 966 | = | 1 | remainder ( 483 ) | ||||||||||||||||
| 966 | : | 483 | = | 2 | remainder ( 0 ) | ||||||||||||||||
| GCD = 483 | |||||||||||||||||||||
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.