The distinct prime factors of 18 are 2 and 3 . What is the sum of all of the distinct prime factors of $4446 ?$
The positive integer 4446 is even and the sum of its digits is $4+4+4+6=18$ which is a multiple of 9 , so 4446 itself is divisible by both 2 and 9 . (Similar to the well-known divisibility rule for 3 , a positive integer is divisible by 9 exactly when the sum of its digits is divisible by 9.)

Factoring, we have $4446=2 \times 3^{2} \times 247$, and it can be checked that $247=13 \times 19$.

Therefore, $4446=2 \times 3^{2} \times 13 \times 19$, so the distinct prime factors of 4446 are 2, 3, 13, and 19, the sum of which is 37 .

ANSWER: 37