70 (number)

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69 70 71
Cardinal seventy
Ordinal 70th
(seventieth)
Factorization 2 · 5 · 7
Divisors 1, 2, 5, 7, 10, 14, 35, 70
Roman numeral LXX
Binary 10001102
Ternary 21213
Quaternary 10124
Quinary 2405
Senary 1546
Octal 1068
Duodecimal 5A12
Hexadecimal 4616
Vigesimal 3A20
Base 36 1Y36
Hebrew ע (Ayin)

70 (seventy) is the natural number following 69 and preceding 71.

In mathematics[edit]

Its factorization makes it a sphenic number. 70 is a Pell number and a generalized heptagonal number, one of only two numbers to be both.[1] Also, it is the seventh pentagonal number and the fourth triskaidecagonal number, as well as the fifth pentatope number. It is the smallest weird number.

The sum of the first twenty four squares starting from one is seventy squared. This relates seventy to the Leech lattice and thus string theory.

Since it is possible to find sequences of 70 consecutive integers such that each inner member shares a factor with either the first or the last member, 70 is an Erdős–Woods number.

In base 10, it is a Harshad number.

In science[edit]

Astronomy[edit]

In religion[edit]

In law[edit]

In sports[edit]

In other fields[edit]

70 is:

Number name[edit]

Main article: number name

The French do not have a word for 70, instead using "soixante-dix" (60 + 10). Other French-speaking countries such as Belgium, Switzerland, Aosta Valley and Jersey do have a word for it, using "septante."[4]

Notes[edit]

  1. ^ Rao, B. Srinivasa (2005), "Heptagonal Numbers in the Pell Sequence and Diophantine Equations 2x2 = y2(5y − 3)2 ± 2", Fibonacci Quarterly 43 (3): 194–201 .
  2. ^ The Official Highway Code, pub. Department for Transport (Revised 2007 Edition). ISBN 978-0-11-552814-9. A white circular sign with a black diagonal stripe indicates that the national speed limit applies. This depends on the vehicle type and grade of road. The table on p.40 shows the highest speed permitted to be 70mph, for normally-laden cars and motorcycles on dual-carriageways and motorways.
  3. ^ Guxi in Baidu Encyclopedia (Chinese: 七十岁,古来稀)
  4. ^ Peter Higgins, Number Story. London: Copernicus Books (2008): 19. "Belgian French speakers however grew tired of this and introduced the new names septante, octante, nonante etc. for these numbers".