75 (number)

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

← 74 75 76 →
Cardinalseventy-five
Ordinal75th
(seventy-fifth)
Factorization3 × 52
Divisors1, 3, 5, 15, 25, 75
Greek numeralΟΕ´
Roman numeralLXXV
Binary10010112
Ternary22103
Senary2036
Octal1138
Duodecimal6312
Hexadecimal4B16

In mathematics

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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

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Seventy-five is:

References

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  1. ^ Sloane, N. J. A. (ed.). "Sequence A003052". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  2. ^ Sloane, N. J. A. (ed.). "Sequence A001106". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  3. ^ Sloane, N. J. A. (ed.). "Sequence A002411". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A007629". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
  5. ^ Sloane, N. J. A. (ed.). "Sequence A000670". 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.