The GCD of given numbers is 3.
Step 1 :
Divide $ 123 $ by $ 36 $ and get the remainder
The remainder is positive ($ 15 > 0 $), so we will continue with division.
Step 2 :
Divide $ 36 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is still positive ($ 6 > 0 $), so we will continue with division.
Step 3 :
Divide $ 15 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 4 :
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.
123 | : | 36 | = | 3 | remainder ( 15 ) | ||||||
36 | : | 15 | = | 2 | remainder ( 6 ) | ||||||
15 | : | 6 | = | 2 | 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.