The GCD of given numbers is 3.
Step 1 :
Divide $ 162 $ by $ 39 $ and get the remainder
The remainder is positive ($ 6 > 0 $), so we will continue with division.
Step 2 :
Divide $ 39 $ by $ \color{blue}{ 6 } $ and get the remainder
The remainder is still positive ($ 3 > 0 $), so we will continue with division.
Step 3 :
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.
162 | : | 39 | = | 4 | remainder ( 6 ) | ||||
39 | : | 6 | = | 6 | 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.