The GCD of given numbers is 15.
Step 1 :
Divide $ 195 $ by $ 45 $ and get the remainder
The remainder is positive ($ 15 > 0 $), so we will continue with division.
Step 2 :
Divide $ 45 $ 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.
195 | : | 45 | = | 4 | remainder ( 15 ) | ||
45 | : | 15 | = | 3 | remainder ( 0 ) | ||
GCD = 15 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.