Consider numbers like 54 and 90.
In the lists of all divisors (for each of those two) 9 distinct digits appear!

54: (1,2,3,6,9,18,27,54); all digits , except 0
90: (1,2,3,5,6,9,10,15,18,30,45,90); 7 excluded

List all such numbers below 1000.