Four of them.
1111 is the only one.
There are uncountably infinitely many real numbers between 1080 and 1100. There are 21 integers between 1080 and 1100, including the "endpoints." They are: 1080, 1081, 1082, 1083, 1084, 1085, 1086, 1087, 1088, 1089, 1090, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1098, 1099, 1100.
1100
There are 19 numbers between zero and 365 that have an odd number of factors.
There are 11 numbers between 1 and 130 that have an odd number of factors: 1,4,9,16,25,36,49,64,81,100,121.
There are seven: 1057, 1064, 1071, 1078, 1085, 1092, 1099.
All of the odd numbers in that range can be factors.
There are three of them with exactly five factors.
Three numbers.
50
2100
All numbers have factors.