The GCD of given numbers is 1.
Step 1 :
Divide $ 2000 $ by $ 1713 $ and get the remainder
The remainder is positive ($ 287 > 0 $), so we will continue with division.
Step 2 :
Divide $ 1713 $ by $ \color{blue}{ 287 } $ and get the remainder
The remainder is still positive ($ 278 > 0 $), so we will continue with division.
Step 3 :
Divide $ 287 $ by $ \color{blue}{ 278 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 4 :
Divide $ 278 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 8 > 0 $), so we will continue with division.
Step 5 :
Divide $ 9 $ by $ \color{blue}{ 8 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 6 :
Divide $ 8 $ 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.
2000 | : | 1713 | = | 1 | remainder ( 287 ) | ||||||||||
1713 | : | 287 | = | 5 | remainder ( 278 ) | ||||||||||
287 | : | 278 | = | 1 | remainder ( 9 ) | ||||||||||
278 | : | 9 | = | 30 | remainder ( 8 ) | ||||||||||
9 | : | 8 | = | 1 | remainder ( 1 ) | ||||||||||
8 | : | 1 | = | 8 | remainder ( 0 ) | ||||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.