168 (number)

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← 167 168 169 →
Cardinal one hundred sixty-eight
Ordinal 168th
(one hundred sixty-eighth)
Factorization 23 × 3 × 7
Divisors 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
Greek numeral ΡΞΗ´
Roman numeral CLXVIII, clxviii
Binary 101010002
Ternary 200203
Senary 4406
Octal 2508
Duodecimal 12012
Hexadecimal A816

168 (one hundred [and] sixty-eight) is the natural number following 167 and preceding 169.

Contents

Mathematics

168 is a Dedekind number, [1] and an idoneal numbers, and a Cunningham number,. [2]

Abstract algebra

168 is the order of the second smallest nonabelian simple group From Hurwitz's automorphisms theorem, 168 is the maximum possible number of automorphisms of a genus 3 Riemann surface, this maximum being achieved by the Klein quartic, whose symmetry group is . [3]

In other fields

Numerology

Some Chinese consider 168 a lucky number, because 一六八 ("168") Mandarin pinyin :yīliùbā is roughly homophonous with the phrase "一路發" Mandarin pinyin :yīlùfā which means "fortune all the way", or, as the United States Mint claims, "Prosperity Forever". [4]

References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA000372(Dedekind numbers: number of monotone Boolean functions of n variables, number of antichains of subsets of an n-set, number of elements in a free distributive lattice on n generators, number of Sperner families.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-04-01.
  2. ↑ "Sloane's A000926 : Euler's "numerus idoneus" (or "numeri idonei", or idoneal, or suitable, or convenient numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  3. ↑ "week214". math.ucr.edu. Retrieved 9 April 2023.
  4. ↑ "$1 Prosperity Forever 168 Note - US Mint" . Retrieved 9 April 2023.
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