128 (number)

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← 127 128 129 →
Cardinal one hundred twenty-eight
Ordinal 128th
(one hundred twenty-eighth)
Factorization 27
Divisors 1, 2, 4, 8, 16, 32, 64, 128
Greek numeral ΡΚΗ´
Roman numeral CXXVIII
Binary 100000002
Ternary 112023
Quaternary 20004
Quinary 10035
Senary 3326
Octal 2008
Duodecimal A812
Hexadecimal 8016
Vigesimal 6820
Base 36 3K36

128 (one hundred [and] twenty-eight) is the natural number following 127 and preceding 129.

In mathematics[edit]

128 is the seventh power of 2. It is the largest number which cannot be expressed as the sum of any number of distinct squares,[1][2] but it is divisible by the total number of its divisors, making it a refactorable number.[3]

The sum of Euler's totient function φ(x) over the first twenty integers is 128.[4]

128 can be expressed by a combination of its digits with mathematical operators thus 128 = 28 - 1, making it a Friedman number in base 10.[5]

A hepteract has 128 vertices.

128 is the only 3-digit number that is a 7th power (27).

In bar codes[edit]

  • Code 128 is a Uniform Symbology Specification (USS Code 128) alphanumeric bar code that encodes text, numbers, numerous functions, and designed to encode all 128 ASCII characters (ASCII 0 to ASCII 127), as used in the shipping industry.
  • Subdivisions include:

In computing[edit]

In the military[edit]

In transportation[edit]

In other fields[edit]

One hundred [and] twenty-eight is also:

See also[edit]

Notes[edit]

  1. ^ Sprague, R. (1948), "Über Zerlegungen in ungleiche Quadratzahlen", Math. Z., 51 (3): 289–290, MR 0027285, doi:10.1007/BF01181594 
  2. ^ OEIS:A001422. Similarly, the largest numbers that cannot be expressed as sums of distinct cubes and fourth powers, respectively, are 12758 and 5134240 (sequence A001661 in the OEIS).
  3. ^ OEIS:A033950.
  4. ^ OEIS:A002088.
  5. ^ OEIS:A036057.

References[edit]

External links[edit]