The GCD of given numbers is 3.
Step 1 :
Divide $ 10254 $ by $ 789 $ and get the remainder
The remainder is positive ($ 786 > 0 $), so we will continue with division.
Step 2 :
Divide $ 789 $ by $ \color{blue}{ 786 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 3 :
Divide $ 786 $ by $ \color{blue}{ 3 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 3 }} $.
We can summarize an algorithm into a following table.
10254 | : | 789 | = | 12 | remainder ( 786 ) | ||||
789 | : | 786 | = | 1 | remainder ( 3 ) | ||||
786 | : | 3 | = | 262 | remainder ( 0 ) | ||||
GCD = 3 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.