Calculate φ(143)

__Step 1: calculate factors for 143__Using our

factor calculator, we see that the factors for 143 are 1,11,13,143

__Step 2: Find the factors of all numbers less than 143 which have only 1 as a common factor:__Number | Factor List | Matching Factors with 143 | Add to Totient List? |
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1 | 1 | 1 | Y |

2 | 1,2 | 1 | Y |

3 | 1,3 | 1 | Y |

4 | 1,2,4 | 1 | Y |

5 | 1,5 | 1 | Y |

6 | 1,2,3,6 | 1 | Y |

7 | 1,7 | 1 | Y |

8 | 1,2,4,8 | 1 | Y |

9 | 1,3,9 | 1 | Y |

10 | 1,2,5,10 | 1 | Y |

11 | 1,11 | 1,11 | N |

12 | 1,2,3,4,6,12 | 1 | Y |

13 | 1,13 | 1,13 | N |

14 | 1,2,7,14 | 1 | Y |

15 | 1,3,5,15 | 1 | Y |

16 | 1,2,4,8,16 | 1 | Y |

17 | 1,17 | 1 | Y |

18 | 1,2,3,6,9,18 | 1 | Y |

19 | 1,19 | 1 | Y |

20 | 1,2,4,5,10,20 | 1 | Y |

21 | 1,3,7,21 | 1 | Y |

22 | 1,2,11,22 | 1,11 | N |

23 | 1,23 | 1 | Y |

24 | 1,2,3,4,6,8,12,24 | 1 | Y |

25 | 1,5,25 | 1 | Y |

26 | 1,2,13,26 | 1,13 | N |

27 | 1,3,9,27 | 1 | Y |

28 | 1,2,4,7,14,28 | 1 | Y |

29 | 1,29 | 1 | Y |

30 | 1,2,3,5,6,10,15,30 | 1 | Y |

31 | 1,31 | 1 | Y |

32 | 1,2,4,8,16,32 | 1 | Y |

33 | 1,3,11,33 | 1,11 | N |

34 | 1,2,17,34 | 1 | Y |

35 | 1,5,7,35 | 1 | Y |

36 | 1,2,3,4,6,9,12,18,36 | 1 | Y |

37 | 1,37 | 1 | Y |

38 | 1,2,19,38 | 1 | Y |

39 | 1,3,13,39 | 1,13 | N |

40 | 1,2,4,5,8,10,20,40 | 1 | Y |

41 | 1,41 | 1 | Y |

42 | 1,2,3,6,7,14,21,42 | 1 | Y |

43 | 1,43 | 1 | Y |

44 | 1,2,4,11,22,44 | 1,11 | N |

45 | 1,3,5,9,15,45 | 1 | Y |

46 | 1,2,23,46 | 1 | Y |

47 | 1,47 | 1 | Y |

48 | 1,2,3,4,6,8,12,16,24,48 | 1 | Y |

49 | 1,7,49 | 1 | Y |

50 | 1,2,5,10,25,50 | 1 | Y |

51 | 1,3,17,51 | 1 | Y |

52 | 1,2,4,13,26,52 | 1,13 | N |

53 | 1,53 | 1 | Y |

54 | 1,2,3,6,9,18,27,54 | 1 | Y |

55 | 1,5,11,55 | 1,11 | N |

56 | 1,2,4,7,8,14,28,56 | 1 | Y |

57 | 1,3,19,57 | 1 | Y |

58 | 1,2,29,58 | 1 | Y |

59 | 1,59 | 1 | Y |

60 | 1,2,3,4,5,6,10,12,15,20,30,60 | 1 | Y |

61 | 1,61 | 1 | Y |

62 | 1,2,31,62 | 1 | Y |

63 | 1,3,7,9,21,63 | 1 | Y |

64 | 1,2,4,8,16,32,64 | 1 | Y |

65 | 1,5,13,65 | 1,13 | N |

66 | 1,2,3,6,11,22,33,66 | 1,11 | N |

67 | 1,67 | 1 | Y |

68 | 1,2,4,17,34,68 | 1 | Y |

69 | 1,3,23,69 | 1 | Y |

70 | 1,2,5,7,10,14,35,70 | 1 | Y |

71 | 1,71 | 1 | Y |

72 | 1,2,3,4,6,8,9,12,18,24,36,72 | 1 | Y |

73 | 1,73 | 1 | Y |

74 | 1,2,37,74 | 1 | Y |

75 | 1,3,5,15,25,75 | 1 | Y |

76 | 1,2,4,19,38,76 | 1 | Y |

77 | 1,7,11,77 | 1,11 | N |

78 | 1,2,3,6,13,26,39,78 | 1,13 | N |

79 | 1,79 | 1 | Y |

80 | 1,2,4,5,8,10,16,20,40,80 | 1 | Y |

81 | 1,3,9,27,81 | 1 | Y |

82 | 1,2,41,82 | 1 | Y |

83 | 1,83 | 1 | Y |

84 | 1,2,3,4,6,7,12,14,21,28,42,84 | 1 | Y |

85 | 1,5,17,85 | 1 | Y |

86 | 1,2,43,86 | 1 | Y |

87 | 1,3,29,87 | 1 | Y |

88 | 1,2,4,8,11,22,44,88 | 1,11 | N |

89 | 1,89 | 1 | Y |

90 | 1,2,3,5,6,9,10,15,18,30,45,90 | 1 | Y |

91 | 1,7,13,91 | 1,13 | N |

92 | 1,2,4,23,46,92 | 1 | Y |

93 | 1,3,31,93 | 1 | Y |

94 | 1,2,47,94 | 1 | Y |

95 | 1,5,19,95 | 1 | Y |

96 | 1,2,3,4,6,8,12,16,24,32,48,96 | 1 | Y |

97 | 1,97 | 1 | Y |

98 | 1,2,7,14,49,98 | 1 | Y |

99 | 1,3,9,11,33,99 | 1,11 | N |

100 | 1,2,4,5,10,20,25,50,100 | 1 | Y |

101 | 1,101 | 1 | Y |

102 | 1,2,3,6,17,34,51,102 | 1 | Y |

103 | 1,103 | 1 | Y |

104 | 1,2,4,8,13,26,52,104 | 1,13 | N |

105 | 1,3,5,7,15,21,35,105 | 1 | Y |

106 | 1,2,53,106 | 1 | Y |

107 | 1,107 | 1 | Y |

108 | 1,2,3,4,6,9,12,18,27,36,54,108 | 1 | Y |

109 | 1,109 | 1 | Y |

110 | 1,2,5,10,11,22,55,110 | 1,11 | N |

111 | 1,3,37,111 | 1 | Y |

112 | 1,2,4,7,8,14,16,28,56,112 | 1 | Y |

113 | 1,113 | 1 | Y |

114 | 1,2,3,6,19,38,57,114 | 1 | Y |

115 | 1,5,23,115 | 1 | Y |

116 | 1,2,4,29,58,116 | 1 | Y |

117 | 1,3,9,13,39,117 | 1,13 | N |

118 | 1,2,59,118 | 1 | Y |

119 | 1,7,17,119 | 1 | Y |

120 | 1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120 | 1 | Y |

121 | 1,11,121 | 1,11 | N |

122 | 1,2,61,122 | 1 | Y |

123 | 1,3,41,123 | 1 | Y |

124 | 1,2,4,31,62,124 | 1 | Y |

125 | 1,5,25,125 | 1 | Y |

126 | 1,2,3,6,7,9,14,18,21,42,63,126 | 1 | Y |

127 | 1,127 | 1 | Y |

128 | 1,2,4,8,16,32,64,128 | 1 | Y |

129 | 1,3,43,129 | 1 | Y |

130 | 1,2,5,10,13,26,65,130 | 1,13 | N |

131 | 1,131 | 1 | Y |

132 | 1,2,3,4,6,11,12,22,33,44,66,132 | 1,11 | N |

133 | 1,7,19,133 | 1 | Y |

134 | 1,2,67,134 | 1 | Y |

135 | 1,3,5,9,15,27,45,135 | 1 | Y |

136 | 1,2,4,8,17,34,68,136 | 1 | Y |

137 | 1,137 | 1 | Y |

138 | 1,2,3,6,23,46,69,138 | 1 | Y |

139 | 1,139 | 1 | Y |

140 | 1,2,4,5,7,10,14,20,28,35,70,140 | 1 | Y |

141 | 1,3,47,141 | 1 | Y |

142 | 1,2,71,142 | 1 | Y |

The following numbers only had 1 as a common factor

1,2,3,4,5,6,7,8,9,10,12,14,15,16,17,18,19,20,21,23,24,25,27,28,29,30,31,32,34,35,36,37,38,40,41,42,43,45,46,47,48,49,50,51,53,54,56,57,58,59,60,61,62,63,64,67,68,69,70,71,72,73,74,75,76,79,80,81,82,83,84,85,86,87,89,90,92,93,94,95,96,97,98,100,101,102,103,105,106,107,108,109,111,112,113,114,115,116,118,119,120,122,123,124,125,126,127,128,129,131,133,134,135,136,137,138,139,140,141,142

From our list above, we see that φ(143) =

**120**