The GCD of given numbers is 15.
Step 1 :
Divide $ 165 $ by $ 135 $ and get the remainder
The remainder is positive ($ 30 > 0 $), so we will continue with division.
Step 2 :
Divide $ 135 $ by $ \color{blue}{ 30 } $ and get the remainder
The remainder is still positive ($ 15 > 0 $), so we will continue with division.
Step 3 :
Divide $ 30 $ by $ \color{blue}{ 15 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 15 }} $.
We can summarize an algorithm into a following table.
165 | : | 135 | = | 1 | remainder ( 30 ) | ||||
135 | : | 30 | = | 4 | remainder ( 15 ) | ||||
30 | : | 15 | = | 2 | remainder ( 0 ) | ||||
GCD = 15 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.