96 (number)

← 95 96 97 →
Cardinalninety-six
Ordinal96th
(ninety-sixth)
Factorization25 × 3
Divisors1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Greek numeralϞϚ´
Roman numeralXCVI
Binary11000002
Ternary101203
Senary2406
Octal1408
Duodecimal8012
Hexadecimal6016

96 (ninety-six) is the natural number following 95 and preceding 97. It is a number that appears the same when turned upside down.

In mathematics

96 as the difference of two squares (in orange).

96 is:

  • an octagonal number.[1]
  • a refactorable number.[2]
  • an untouchable number.[3]
  • a semiperfect number since it is a multiple of 6.
  • an abundant number since the sum of its proper divisors is greater than 96.
  • the fourth Granville number and the second non-perfect Granville number. The next Granville number is 126, the previous being 24.
  • the sum of Euler's totient function φ(x) over the first seventeen integers.
  • strobogrammatic in bases 10 (9610), 11 (8811) and 95 (1195).
  • palindromic in bases 11 (8811), 15 (6615), 23 (4423), 31 (3331), 47 (2247) and 95 (1195).
  • an Erdős–Woods number, since it is possible to find sequences of 96 consecutive integers such that each inner member shares a factor with either the first or the last member.[4]
  • divisible by the number of prime numbers (24) below 96.
  • the smallest natural number that can be expressed as the difference of two nonzero squares in more than three ways: , , or .[5]

Skilling's figure, a degenerate uniform polyhedron, has a Euler characteristic

Every integer greater than 96 may be represented as a sum of distinct super-prime numbers.

In geography

  • Ninety Six, South Carolina
  • Ninety Six District, a historical judicial and military district of colonial America which extended through North and South Carolina
  • Ninety Six National Historic Site, in Ninety Six, South Carolina, derives its name from the original settlement's distance in miles from a Cherokee village in the Blue Ridge Mountains

In music

In science

In other fields

See also

References

  1. ^ "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  2. ^ "Sloane's A033950 : Refactorable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  3. ^ "Sloane's A005114 : Untouchable numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  4. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A334078". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

External links

  • On the number 96
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