A nasty number is a positive integer having at least four different factors such that the difference between one pair of factors equals the sum of another pair of factors. For instance,

6 is nasty because 6 – 1 = 2 + 3

24 is nasty because 12 – 2 = 4 + 6

30 is nasty because 15 – 2 = 10 + 3.

Find the other six nasty numbers that are less than 180.

54 is nasty because 18 – 3 = 6 + 9

60 is nasty because 20 – 3 = 12 + 5

96 is nasty because 24 – 4 = 12 + 8

120 is nasty because 30 – 4 = 20 + 6

150 is nasty because 30 – 5 = 10 + 15

180 is nasty because 45 – 4 = 36 + 5