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((refimprove|date=December 2012))
((Infobox number
| number = 170
| 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 [[factorial]] can be stored in [[Double-precision_floating-point_format#IEEE_754_double-precision_binary_floating-point_format:_binary64|IEEE 754 double-precision floating-point format]]. This is probably why it is also the largest [[factorial]] that [[Google]]'s built-in [[calculator]] will calculate, returning the answer as 170! = 7.25741562 × 10<sup>306</sup>.((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>

==See also==
* [[170s]]
* [[E170 (disambiguation)]]
* [[F170 (disambiguation)]]
* [[List of highways numbered 170]]
* [[List of United States Supreme Court cases, volume 170|United States Supreme Court cases, Volume 170]]
* [[United Nations Security Council Resolution 170]]
* [[Pennsylvania House of Representatives, District 170]]

==References==
((reflist))

==External links==
((Commons cat))
* [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]

((Integers|1))

((DEFAULTSORT:170 (Number)))
[[Category:Integers]]

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170 (number) (edit)
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