167 168 169
Cardinalone hundred sixty-eight
Ordinal168th
(one hundred sixty-eighth)
Factorization23 × 3 × 7
Divisors1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
Greek numeralΡΞΗ´
Roman numeralCLXVIII
Binary101010002
Ternary200203
Senary4406
Octal2508
Duodecimal12012
HexadecimalA816

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

In mathematics

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 largest known n such that 2n does not contain all decimal digits.[3]

168 is the fourth Dedekind number.

In astronomy

In the military

In movies

In transportation

In other fields

168 is also:

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

See also

References

  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. "week214". math.ucr.edu. Retrieved 9 April 2023.
  3. "Sloane's A130696: Numbers k such that 2^k does not contain all ten decimal digits". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-12-19.
  4. "$1 Prosperity Forever 168 Note - US Mint". Retrieved 9 April 2023.
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