75 (number)

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← 74 75 76 →
Cardinal seventy-five
Ordinal 75th
(seventy-fifth)
Factorization 3 × 52
Divisors 1, 3, 5, 15, 25, 75
Greek numeral ΟΕ´
Roman numeral LXXV
Binary 10010112
Ternary 22103
Senary 2036
Octal 1138
Duodecimal 6312
Hexadecimal 4B16

75 (seventy-five) is the natural number following 74 and preceding 76.

Contents

In mathematics

75 is a self number because there is no integer that added up to its own digits adds up to 75. [1] It is the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number, as well as a nonagonal number. [2] [3]

It is also the fourth ordered Bell number, and a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 7, 5, 12, 17, 29, 46, 75... [4]

75 is the count of the number of weak orderings on a set of four items. [5]

Excluding the infinite sets, there are 75 uniform polyhedra in the third dimension, which incorporate star polyhedra as well. Inclusive of 7 families of prisms and antiprisms, there are also 75 uniform compound polyhedra.

In other fields

Seventy-five is:

Related Research Articles

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<span class="mw-page-title-main">5</span> Integer number 5

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References

  1. ↑ Sloane, N. J. A. (ed.). "SequenceA003052". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  2. ↑ Sloane, N. J. A. (ed.). "SequenceA001106". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  3. ↑ Sloane, N. J. A. (ed.). "SequenceA002411". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  4. ↑ Sloane, N. J. A. (ed.). "SequenceA007629". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  5. ↑ Sloane, N. J. A. (ed.). "SequenceA000670". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
  6. ↑ “Who are our senators and what do they do?”, Parliament of Canada, retrieved 2014-02-02.
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