The GCD of given numbers is 17.
Step 1 :
Divide $ 42823 $ by $ 6409 $ and get the remainder
The remainder is positive ($ 4369 > 0 $), so we will continue with division.
Step 2 :
Divide $ 6409 $ by $ \color{blue}{ 4369 } $ and get the remainder
The remainder is still positive ($ 2040 > 0 $), so we will continue with division.
Step 3 :
Divide $ 4369 $ by $ \color{blue}{ 2040 } $ and get the remainder
The remainder is still positive ($ 289 > 0 $), so we will continue with division.
Step 4 :
Divide $ 2040 $ by $ \color{blue}{ 289 } $ and get the remainder
The remainder is still positive ($ 17 > 0 $), so we will continue with division.
Step 5 :
Divide $ 289 $ by $ \color{blue}{ 17 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 17 }} $.
We can summarize an algorithm into a following table.
42823 | : | 6409 | = | 6 | remainder ( 4369 ) | ||||||||
6409 | : | 4369 | = | 1 | remainder ( 2040 ) | ||||||||
4369 | : | 2040 | = | 2 | remainder ( 289 ) | ||||||||
2040 | : | 289 | = | 7 | remainder ( 17 ) | ||||||||
289 | : | 17 | = | 17 | remainder ( 0 ) | ||||||||
GCD = 17 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.