List of Prime Factorizations of Integers from 2 to 200

For your convenience, I have listed the unique prime factorizations of integers from 2 to 200. To make it look more compact, repeated prime numbers are expressed in exponential forms.


  • 2 is prime.
  • 3 is prime.
  • 4 = {2^2}
  • 5 is prime.
  • 6 = 2 \cdot 3
  • 7 is prime.
  • 8 = {2^3}
  • 9 = {3^2}
  • 10 = 2 \cdot 5
  • 11 is prime.
  • 12 = {2^2} \cdot 3
  • 13 is prime.
  • 14 = 2 \cdot 7
  • 15 = 3 \cdot 5

  • 16 = {2^4}
  • 17 is prime.
  • 18 = 2 \cdot {3^2}
  • 19 is prime.
  • 20 = {2^2} \cdot 5
  • 21 = 3 \cdot 7
  • 22 = 2 \cdot 11
  • 23 is prime.
  • 24 = {2^3} \cdot 3
  • 25 = {5^2}

  • 26 = 2 \cdot 13
  • 27 = {3^3}
  • 28 = {2^2} \cdot 7
  • 29 is prime.
  • 30 = 2 \cdot 3 \cdot 5
  • 31 is prime.
  • 32 = {2^5}
  • 33 = 3 \cdot 11
  • 34 = 2 \cdot 17
  • 35 = 5 \cdot 7

  • 36 = {2^2} \cdot {3^2}
  • 37 is prime.
  • 38 = 2 \cdot 19
  • 39 is prime.
  • 40 = {2^3} \cdot 5
  • 41 is prime.
  • 42 = 2 \cdot 3 \cdot 7
  • 43 is prime.
  • 44 = {2^2} \cdot 11
  • 45 = {3^2} \cdot 5
  • 46 = 2 \cdot 23
  • 47 is prime.
  • 48 = {2^4} \cdot 3

  • 49 = {7^2}
  • 50 = 2 \cdot {5^2}
  • 51 = 3 \cdot 17
  • 52 = {2^2} \cdot 13
  • 53 is prime.
  • 54 = 2 \cdot {3^3}
  • 55 = 5 \cdot 11
  • 56 = {2^3} \cdot 7
  • 57 = 3 \cdot 19
  • 58 = 2 \cdot 29
  • 59 is prime.
  • 60 = {2^2} \cdot 3 \cdot 5
  • 61 is prime.
  • 62 = 2 \cdot 31
  • 63 = {3^2} \cdot 7
  • 64 = {2^6}
  • 65 = 5 \cdot 13
  • 66 = 2 \cdot 3 \cdot 11
  • 67 is prime.
  • 68 = {2^2} \cdot 17
  • 69 = 3 \cdot 23
  • 70 = 2 \cdot 5 \cdot 7
  • 71 is prime.
  • 72 = {2^3} \cdot {3^2}
  • 73 is prime.
  • 74 = 2 \cdot 37
  • 75 = 3 \cdot {5^2}

  • 76 = {2^2} \cdot 19
  • 77 = 7 \cdot 11
  • 78 = 2 \cdot 3 \cdot 13
  • 79 is prime.
  • 80 = {2^4} \cdot 5
  • 81 = {3^4}
  • 82 = 2 \cdot 41
  • 83 is prime.
  • 84 = {2^2} \cdot 3 \cdot 7
  • 85 = 5 \cdot 17
  • 86 = 2 \cdot 43
  • 87 = 3 \cdot 29
  • 88 = {2^3} \cdot 11
  • 89 is prime.
  • 90 = 2 \cdot {3^2} \cdot 5
  • 91 = 7 \cdot 13
  • 92 = {2^2} \cdot 23
  • 93 = 3 \cdot 31
  • 94 = 2 \cdot 47
  • 95 = 5 \cdot 19
  • 96 = {2^5} \cdot 3
  • 97 is prime.
  • 98 = 2 \cdot {7^2}
  • 99 = {3^2} \cdot 11
  • 100 = {2^2} \cdot {5^2}
  • 101 is prime.
  • 102 = 2 \cdot 3 \cdot 17
  • 103 is prime.
  • 104 = {2^3} \cdot 13
  • 105 = 3 \cdot 5 \cdot 7
  • 106 = 2 \cdot 53
  • 107 is prime.
  • 108 = {2^2} \cdot {3^3}
  • 109 is prime.
  • 110 = 2 \cdot 5 \cdot 11
  • 111 = 3 \cdot 37
  • 112 = {2^4} \cdot 7
  • 113 is prime.
  • 114 = 2 \cdot 3 \cdot 19
  • 115 = 5 \cdot 23
  • 116 = {2^2} \cdot 29
  • 117 = {3^2} \cdot 13
  • 118 = 2 \cdot 59
  • 119 = 7 \cdot 17
  • 120 = {2^3} \cdot 3 \cdot 5
  • 121 = {11^2}
  • 122 = 2 \cdot 61
  • 123 = 3 \cdot 41
  • 124 = {2^2} \cdot 31
  • 125 = {5^3}
  • 126 = 2 \cdot {3^2} \cdot 7
  • 127 is prime.
  • 128 = {2^7}
  • 129 = 3 \cdot 43
  • 130 = 2 \cdot 5 \cdot 13
  • 131 is prime.
  • 132 = {2^2} \cdot 3 \cdot 11
  • 133 = 7 \cdot 19
  • 134 = 2 \cdot 67
  • 135 = {3^3} \cdot 5
  • 136 = {2^3} \cdot 17
  • 137 is prime.
  • 138 = 2 \cdot 3 \cdot 23
  • 139 is prime.
  • 140 = {2^2} \cdot 5 \cdot 7
  • 141 = 3 \cdot 47
  • 142 = 2 \cdot 71
  • 143 = 11 \cdot 13
  • 144 = {2^4} \cdot {3^2}
  • 145 = 5 \cdot 29
  • 146 = 2 \cdot 73
  • 147 = 3 \cdot {7^2}
  • 148 = {2^2} \cdot 37
  • 149 is prime.
  • 150 = 2 \cdot 3 \cdot {5^2}
  • 151 is prime.
  • 152 = {2^3} \cdot 19
  • 153 = {3^2} \cdot 17
  • 154 = 2 \cdot 7 \cdot 11
  • 155 = 5 \cdot 31
  • 156 = {2^2} \cdot 3 \cdot 13
  • 157 is prime.
  • 158 = 2 \cdot 79
  • 159 = 3 \cdot 53
  • 160 = {2^5} \cdot 5
  • 161 = 7 \cdot 23
  • 162 = 2 \cdot {3^4}
  • 163 is prime.
  • 164 = {2^2} \cdot 41
  • 165 = 3 \cdot 5 \cdot 11
  • 166 = 2 \cdot 83
  • 167 is prime.
  • 168 = {2^3} \cdot 3 \cdot 7
  • 169 = {13^2}
  • 170 = 2 \cdot 5 \cdot 17
  • 171 = {3^2} \cdot 19
  • 172 = {2^2} \cdot 43
  • 173 is prime.
  • 174 = 2 \cdot 3 \cdot 29
  • 175 = {5^2} \cdot 7
  • 176 = {2^4} \cdot 11
  • 177 = 3 \cdot 59
  • 178 = 2 \cdot 89
  • 179 is prime.
  • 180 = {2^2} \cdot {3^2} \cdot 5
  • 181 is prime.
  • 182 = 2 \cdot 7 \cdot 13
  • 183 = 3 \cdot 61
  • 184 = {2^3} \cdot 23
  • 185 = 5 \cdot 37
  • 186 = 2 \cdot 3 \cdot 31
  • 187 = 11 \cdot 17
  • 188 = {2^2} \cdot 47
  • 189 = {3^3} \cdot 7
  • 190 = 2 \cdot 5 \cdot 19
  • 191 is prime.
  • 192 = {2^6} \cdot 3
  • 193 is prime.
  • 194 = 2 \cdot 97
  • 195 = 3 \cdot 5 \cdot 13
  • 196 = {2^2} \cdot {7^2}
  • 197 is prime.
  • 198 = 2 \cdot {3^2} \cdot 11
  • 199 is prime.
  • 200 = {2^3} \cdot {5^2}

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