The GCD of given numbers is 12.
Step 1 :
Divide $ 156 $ by $ 108 $ and get the remainder
The remainder is positive ($ 48 > 0 $), so we will continue with division.
Step 2 :
Divide $ 108 $ by $ \color{blue}{ 48 } $ and get the remainder
The remainder is still positive ($ 12 > 0 $), so we will continue with division.
Step 3 :
Divide $ 48 $ by $ \color{blue}{ 12 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 12 }} $.
We can summarize an algorithm into a following table.
156 | : | 108 | = | 1 | remainder ( 48 ) | ||||
108 | : | 48 | = | 2 | remainder ( 12 ) | ||||
48 | : | 12 | = | 4 | remainder ( 0 ) | ||||
GCD = 12 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.