The GCD of given numbers is 1.
Step 1 :
Divide $ 1000 $ by $ 231 $ and get the remainder
The remainder is positive ($ 76 > 0 $), so we will continue with division.
Step 2 :
Divide $ 231 $ by $ \color{blue}{ 76 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 3 :
Divide $ 76 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is still positive ($ 1 > 0 $), so we will continue with division.
Step 4 :
Divide $ 3 $ 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.
1000 | : | 231 | = | 4 | remainder ( 76 ) | ||||||
231 | : | 76 | = | 3 | remainder ( 3 ) | ||||||
76 | : | 3 | = | 25 | remainder ( 1 ) | ||||||
3 | : | 1 | = | 3 | remainder ( 0 ) | ||||||
GCD = 1 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.