75 (number)
| ||||
|---|---|---|---|---|
| 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 | |||
| Quaternary | 10234 | |||
| Quinary | 3005 | |||
| Senary | 2036 | |||
| Octal | 1138 | |||
| Duodecimal | 6312 | |||
| Hexadecimal | 4B16 | |||
| Vigesimal | 3F20 | |||
| Base 36 | 2336 | |||
75 (seventy-five) is the natural number following 74 and preceding 76.
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:
- The atomic number of rhenium
- The age limit for Canadian senators[6]
- A common name for the Canon de 75 modèle 1897, a French World War I gun
- The department number of the city of Paris
- The number of balls in a standard game of Bingo in the United States
References
- ↑ Sloane, N. J. A., ed. "Sequence A003052". OEIS Foundation. https://oeis.org/A003052.
- ↑ Sloane, N. J. A., ed. "Sequence A001106". OEIS Foundation. https://oeis.org/A001106.
- ↑ Sloane, N. J. A., ed. "Sequence A002411". OEIS Foundation. https://oeis.org/A002411.
- ↑ Sloane, N. J. A., ed. "Sequence A007629". OEIS Foundation. https://oeis.org/A007629.
- ↑ Sloane, N. J. A., ed. "Sequence A000670". OEIS Foundation. https://oeis.org/A000670.
- ↑ “Who are our senators and what do they do?”, Parliament of Canada, retrieved 2014-02-02.
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