48 (number) - Wikipedia

Natural number

← 47 48 49 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-eight
Ordinal	48th(forty-eighth)
Factorization	24 × 3
Divisors	1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Greek numeral	ΜΗ´
Roman numeral	XLVIII, xlviii
Binary	1100002
Ternary	12103
Senary	1206
Octal	608
Duodecimal	4012
Hexadecimal	3016

48 (forty-eight) is the natural number following 47 and preceding 49. It is one third of a gross, or four dozen.

In mathematics

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48 is a highly composite number, and a Størmer number.[1]

By a classical result of Honsberger, the number of incongruent integer-sided triangles of perimeter m {\displaystyle m} is given by the equations m 2 48 {\displaystyle {\tfrac {m^{2}}{48}}} for even m {\displaystyle m} , and ( m + 3 ) 2 48 {\displaystyle {\tfrac {(m+3)^{2}}{48}}} for odd m {\displaystyle m} .[2]

48 is the order of full octahedral symmetry, which describes three-dimensional mirror symmetries associated with the regular octahedron and cube.

There are 48 symmetries of a cube.

In other fields

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Forty-eight may also refer to:

• In Chinese numerology, 48 is an auspicious number meaning 'determined to prosper', or simply 'prosperity', which is good for business.[3]
• '48 is a slang term in Palestinian Arabic for parts of Israel or Palestine not under the control of the State of Palestine. Arab people from those parts are colloquially known as 48-Arabs (Arabic: عرب ٤٨, romanized: ‘Arab Thamāniya wa-Arba‘īn).

References

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1. ^ Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ East, James; Niles, Ron (2019). "Integer polygons of given perimeter". Bulletin of the Australian Mathematical Society. 100 (1). Canberra: Australian Mathematical Society: 131–147. arXiv:1710.11245. doi:10.1017/S0004972718001612. MR 3977311. S2CID 119729735. Zbl 1420.52014.
3. ^ "Chinese Numerology: Lucky and Unlucky Numbers Meaning". My Today's Horoscope. 2019-11-09. Retrieved 2021-09-20.

v t e Z {\displaystyle \mathbb {Z} } Integers
−2, −1
0 to 199 0 to 99 100 to 199  0   1   2   3   4   5   6   7   8   9  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199
200 to 399 200 to 299 300 to 399 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 318 323 325 341 353 359 360 363 365 369 377 384
400 to 999 400s, 500s, and 600s 700s, 800s, and 900s 400 420 440 495 496 500 501 511 512 555 600 610 613 616 666 693 700 720 743 744 777 786 800 801 836 840 880 881 888 900 911 971 987 999
1000s and 10,000s 1000s 1000 1001 1023 1024 1089 1093 1105 1234 1289 1458 1510 1728 1729 1980 1987 2000 2520 3000 3511 4000 5000 5040 6000 6174 7000 7744 7825 8000 8128 8192 9000 9855 9999 10,000s 10,000 16,807 20,000 30,000 40,000 50,000 60,000 64,079 65,535 65,536 65,537 70,000 80,000 90,000
100,000s to 10,000,000,000,000s 100,000 142,857 144,000 1,000,000 10,000,000 43,112,609 100,000,000 1,000,000,000 2,147,483,647 4,294,967,295 10,000,000,000 100,000,000,000 1,000,000,000,000 10,000,000,000,000
Large numbers