The GCD of given numbers is 3.
Step 1 :
Divide $ 54321 $ by $ 9876 $ and get the remainder
The remainder is positive ($ 4941 > 0 $), so we will continue with division.
Step 2 :
Divide $ 9876 $ by $ \color{blue}{ 4941 } $ and get the remainder
The remainder is still positive ($ 4935 > 0 $), so we will continue with division.
Step 3 :
Divide $ 4941 $ by $ \color{blue}{ 4935 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 4 :
Divide $ 4935 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 5 :
Divide $ 6 $ 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.
54321 | : | 9876 | = | 5 | remainder ( 4941 ) | ||||||||
9876 | : | 4941 | = | 1 | remainder ( 4935 ) | ||||||||
4941 | : | 4935 | = | 1 | remainder ( 6 ) | ||||||||
4935 | : | 6 | = | 822 | remainder ( 3 ) | ||||||||
6 | : | 3 | = | 2 | remainder ( 0 ) | ||||||||
GCD = 3 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.