The GCD of given numbers is 3.
Step 1 :
Divide $ 36243 $ by $ 4866 $ and get the remainder
The remainder is positive ($ 2181 > 0 $), so we will continue with division.
Step 2 :
Divide $ 4866 $ by $ \color{blue}{ 2181 } $ and get the remainder
The remainder is still positive ($ 504 > 0 $), so we will continue with division.
Step 3 :
Divide $ 2181 $ by $ \color{blue}{ 504 } $ and get the remainder
The remainder is still positive ($ 165 > 0 $), so we will continue with division.
Step 4 :
Divide $ 504 $ by $ \color{blue}{ 165 } $ and get the remainder
The remainder is still positive ($ 9 > 0 $), so we will continue with division.
Step 5 :
Divide $ 165 $ by $ \color{blue}{ 9 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 6 :
Divide $ 9 $ 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.
36243 | : | 4866 | = | 7 | remainder ( 2181 ) | ||||||||||
4866 | : | 2181 | = | 2 | remainder ( 504 ) | ||||||||||
2181 | : | 504 | = | 4 | remainder ( 165 ) | ||||||||||
504 | : | 165 | = | 3 | remainder ( 9 ) | ||||||||||
165 | : | 9 | = | 18 | remainder ( 3 ) | ||||||||||
9 | : | 3 | = | 3 | remainder ( 0 ) | ||||||||||
GCD = 3 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.