The GCD of given numbers is 25.
Step 1 :
Divide $ 75 $ by $ 50 $ and get the remainder
The remainder is positive ($ 25 > 0 $), so we will continue with division.
Step 2 :
Divide $ 50 $ by $ \color{blue}{ 25 } $ and get the remainder
The remainder is zero => GCD is the last divisor $ \color{blue}{ \boxed { 25 }} $.
We can summarize an algorithm into a following table.
75 | : | 50 | = | 1 | remainder ( 25 ) | ||
50 | : | 25 | = | 2 | remainder ( 0 ) | ||
GCD = 25 |
This solution can be visualized using a Venn diagram.
The GCD equals the product of the numbers at the intersection.