List of Prime Factorizations of Integers from 2 to 200

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


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

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

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

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

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

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

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