170 (number): Difference between revisions - Wikipedia

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{{refimprove|date=December 2012}}

{{Number|number=170▼

{{Infobox number

|cardinal=one hundred [and] seventy

▲{{Number| number = 170

|ordinal=th

| divisor=1, 2, 5, 10, 17, 34, 85, 170▼

|ordinal text=one hundred [and] seventieth

|factorization=<math>2 \cdot 5 \cdot 17</math>

▲|divisor=1, 2, 5, 10, 17, 34, 85, 170

}}

'''170''' ('''one hundred [and] seventy''') is the [[natural number]] following [[169 (number)|169]] and preceding [[171 (number)|171]].

==In mathematics==

170 is the smallest ''n'' for which φ(''n'') and σ(''n'') are both square (64 and 324 respectively). But 170 is never a solution for φ(''x''), making it a [[nontotient]]. Nor is it ever a solution to ''x'' - φ(''x''), making it a [[noncototient]].

170 is a [[repdigit]] in [[base 4]] (2222) and [[base 16]] (AA), as well as in bases 33, 84, and 169. It is also a [[sphenic number]].

170 is the largest integer for which its [[Googlefactorial]]'s built-can be stored in [[calculatorDouble-precision_floating-point_format#IEEE_754_double-precision_binary_floating-point_format:_binary64|IEEE 754 double-precision floating-point format]]. functionThis canis probably why it is computealso the largest [[factorial]] that [[Google]]'s built-in [[calculator]] will calculate, returning the answer as 170! = 7.25741562 × 10³⁰⁶.{{Citation needed|date=April 2021}}

There are 170 different [[cyclic permutation|cyclic]] [[Gilbreath permutation]]s on 12 elements,<ref>{{Cite OEIS|sequencenumber=A000048}}</ref> and therefore there are 170 different [[real number|real]] periodic points of order 12 on the [[Mandelbrot set]].<ref>{{citation|title=Magical Mathematics: the mathematical ideas that animate great magic tricks|first1=Persi|last1=Diaconis|author1-link=Persi Diaconis|first2=Ron|last2=Graham|author2-link=Ronald Graham (mathematician)|publisher=Princeton University Press|year=2012|chapter=Chapter 5: From the Gilbreath Principle to the Mandelbrot Set|pages=61–83}}.</ref>

==In sports==

* 170 is the maximum check-out possible in a standard game of [[darts]] (where the final score must be a double).{{Citation needed|date=May 2010}} It consists of two treble-twenties and a double-bullseye.

==See also==

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* [[United Nations Security Council Resolution 170]]

* [[Pennsylvania House of Representatives, District 170]]

* [[170th meridian west]] and [[170th meridian east]]

==References==

{{reflist}}

==External links==

{{Commons cat|170 (number)}}

* [http://www.numdic.com/170 The Number 170]

* [https://web.archive.org/web/20091023061038/http://athensohio.net/reference/number/170/ Number Facts and Trivia: 170]

* [http://www.positiveintegers.org/170 The Positive Integer 170]

* [http://primes.utm.edu/curios/page.php/170.html Prime curiosities: 170]

* [http://www.bcbuildingtrades.org/pages/careers_plumbers170.htm Plumbers and Pipefitters Union 170, Vancouver, BC]

* [http://www.teamsterlocal170.com Teamsters Local 170, Worcester, MA]

* [http://www.uelocal170.org/ West Virginia Public Workers Union Local 170]

{{Integers|1}}

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{{DEFAULTSORT:170 (Number)}}

[[Category:Integers]]

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