75 (number)

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

← 74 75 76 →
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Cardinal	seventy-five
Ordinal	75th (seventy-fifth)
Factorization	3 × 5^2
Divisors	1, 3, 5, 15, 25, 75
Greek numeral	ΟΕ´
Roman numeral	LXXV
Binary	10010112
Ternary	22103
Octal	1138
Duodecimal	6312
Hexadecimal	4B16

In mathematics

75 is:

• the fourth ordered Bell number, and counts the number of weak orderings on a set of four items.[1]
• the sum of the first five pentagonal numbers, and therefore a pentagonal pyramidal number.[2]
• an nonagonal number.[3]
• 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]
• a self number because there is no integer that added up to its own digits adds up to 75.[5]

Excluding the infinite sets, there are 75 uniform polyhedra (or 76 if edges are allowed to coincide).

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

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