The integers 390 and 9450 have three common positive divisors that are prime numbers. What is the sum of these prime numbers?
We find the prime factorization of 390:

$$
390=39 \cdot 10=3 \cdot 13 \cdot 2 \cdot 5
$$

Since 9450 is divisible by 10 , then 2 and 5 are also prime factors of 9450 .

Since the sum of the digits of 9450 is $9+4+5+0=18$ which is a multiple of 3 , then 9450 is also divisible by 3 .

(We can check that 9450 is not divisible by 13.)

Therefore, the sum of the three common prime divisors of 390 and 9450 is $2+3+5=10$.