The GCD of given numbers is 1.
Step 1 :
Divide $ 4001 $ by $ 2017 $ and get the remainder
The remainder is positive ($ 1984 > 0 $), so we will continue with division.
Step 2 :
Divide $ 2017 $ by $ \color{blue}{ 1984 } $ and get the remainder
The remainder is still positive ($ 33 > 0 $), so we will continue with division.
Step 3 :
Divide $ 1984 $ by $ \color{blue}{ 33 } $ and get the remainder
The remainder is still positive ($ 4 > 0 $), so we will continue with division.
Step 4 :
Divide $ 33 $ by $ \color{blue}{ 4 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 5 :
Divide $ 4 $ 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.
4001 | : | 2017 | = | 1 | remainder ( 1984 ) | ||||||||
2017 | : | 1984 | = | 1 | remainder ( 33 ) | ||||||||
1984 | : | 33 | = | 60 | remainder ( 4 ) | ||||||||
33 | : | 4 | = | 8 | remainder ( 1 ) | ||||||||
4 | : | 1 | = | 4 | remainder ( 0 ) | ||||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.