The GCD of given numbers is 36.
Step 1 :
Divide $ 144 $ by $ 108 $ and get the remainder
The remainder is positive ($ 36 > 0 $), so we will continue with division.
Step 2 :
Divide $ 108 $ by $ \color{blue}{ 36 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 36 }} $.
We can summarize an algorithm into a following table.
144 | : | 108 | = | 1 | remainder ( 36 ) | ||
108 | : | 36 | = | 3 | remainder ( 0 ) | ||
GCD = 36 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.