# 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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Fundamental Theorem of Arithmetic

Prime Factorization of an Integer

List of Prime Factorizations of Integers from 201 to 400

List of Prime Factorizations of Integers from 401 to 600

List of Prime Factorizations of Integers from 601 to 800

List of Prime Factorizations of Integers from 801 to 1,000