The GCD of given numbers is 19.
Step 1 :
Divide $ 133 $ by $ 38 $ and get the remainder
The remainder is positive ($ 19 > 0 $), so we will continue with division.
Step 2 :
Divide $ 38 $ by $ \color{blue}{ 19 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 19 }} $.
We can summarize an algorithm into a following table.
133 | : | 38 | = | 3 | remainder ( 19 ) | ||
38 | : | 19 | = | 2 | remainder ( 0 ) | ||
GCD = 19 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.