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270 (number)

← 269 270 271 →
Cardinaltwo hundred seventy
Ordinal270th
(two hundred seventieth)
Factorization2 × 33 × 5
Greek numeralΣΟ´
Roman numeralCCLXX
Binary1000011102
Ternary1010003
Quaternary100324
Quinary20405
Senary11306
Octal4168
Duodecimal1A612
Hexadecimal10E16
VigesimalDA20
Base 367I36

270 (two hundred [and] seventy) is the natural number following 269 and preceding 271.

In mathematics

  • 270 is a harmonic divisor number[1]
  • 270 is the fourth number that is divisible by its average integer divisor[2]
  • 270 is a practical number, by the second definition
  • The sum of the coprime counts for the first 29 integers is 270
  • 270 is a sparsely totient number, the largest integer with 72 as its totient
  • Given 6 elements, there are 270 square permutations[3]
  • 10! has 270 divisors
  • 270 is a Harshad number in base 10
  • 270 is the smallest positive integer that has divisors ending by digits 1, 2, …, 9.

In other fields

Integers from 271 to 279

271

272

272 = 24·17, sum of four consecutive primes (61 + 67 + 71 + 73), Euler number, primitive semiperfect number, pronic number

273

274

274 = 2·137, tribonacci number, Smith number, nontotient, noncototient, centered triangular number

275

275 = 52·11

276

277

278

278 = 2·139, nontotient

279

279 = 32·31 Every positive integer is the sum of at most 279 eighth powers. See Waring's problem.

References

  1. ^ Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A007340". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A003483". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.