There is no such a number
Numbers having 4 as a factor:
4 has 3 factors- 1,2,4
8 has 4 factors- 1,2,4,8
12 has 6 factors- 1,2,3,4,6,12
etc.
Any number greater than 4 having 4 as a factor, has itself as a factor as well which is greater than 4. The lowest such number is 8 and the larger numbers will have more than 4 factors.