The following all have 3 prime factors, not necessarily distinct:
8 , 12 , 18 , 20 , 27 , 28 , 30 , 42 , 44 , 45 , 50 , 52 , 63 , 66 , 68 , 70 , 75 , 76 , 78 , 92 , 98 , 99 , 102 , 105 , 110 , 114 , 116 , 117 , 124 , 125 , 130 , 138 , 147 , 148 , 153 , 154 , 164 , 165 , 170 , 171 , 172 , 174 , 175 , 182 , 186 , 188 , 190 , 195 , >>Total = 48 such numbers.
+2666 Only square numbers without any factor pairs (other than 1 and itself) work. These are the numbers: 4, 9, 25, 49, 121, and 169, making for a total of \(\color{brown}\boxed{6}\) factors.
