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
Binary 101010002
Ternary 200203
Quaternary 22204
Quinary 11335
Senary 4406
Octal 2508
Duodecimal 12012
Hexadecimal A816
Vigesimal 8820
Base 36 4O36

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

In mathematics[edit]

168 is an even number, a composite number, an abundant number, and an idoneal number.[1]

There are 168 primes less than 1000. 168 is the product of the first two perfect numbers.

168 is the order of the group PSL(2,7), 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 PSL(2,7).[2] The Fano plane has 168 symmetries.

168 is the sum of four consecutive prime numbers: 37 + 41 + 43 + 47.

In astronomy[edit]

In the military[edit]

In movies[edit]

In transportation[edit]

In other fields[edit]

168 is also:

There are 168 pips on a double-six set of dominoes

See also[edit]

References[edit]

  1. ^ "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.
  2. ^ This Week's Finds in Mathematical Physics

External links[edit]