View source for 786 (number)

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'''786''' ('''seven hundred [and] eighty-six''') is the [[natural number]] following [[785 (number)|785]] and preceding [[787 (number)|787]].

==In mathematics==
'''786''' is:
*a [[sphenic number]].
*a [[harshad number]] in bases 4, 5, 7, 14 and 16.
*the [[aliquot sum]] of 510.
*part of the 321329-aliquot tree. The complete aliquot sequence starting at 498 is: 498, 510, '''786''', 798, 1122, 1470, 2634, 2646, 4194, 4932, 7626, 8502, 9978, 9990, 17370, 28026, 35136, 67226, 33616, 37808, 40312, 35288, 37072, 45264, 79728, 146448, 281166, 281178, 363942, 424638, 526338, 722961, 321329, 1, 0

786 might be the largest ''n'' for which the value of the [[central binomial coefficient]] <math>{}_{2n}\!C_n</math> is not divisible by an odd prime squared. If there is a larger such number, it would have to be at least 157450 (see {{OEIS2C|id=A059097}}).

==In other fields==
* In the [[New General Catalogue]], NGC786 is a magnitude 13.5 [[spiral galaxy]] in the constellation [[Aries (constellation)|Aries]]. Additionally, [[786 Bredichina]] is an [[asteroid]].
* In [[juggling]], 786 as fourhanded [[Siteswap]] is also known as French threecount.{{cn|reason=Not mentioned in linked article|date=January 2025}}

==In culture==
[[Islam in India|Indian Muslims]] associate the number with the [[basmala]] by [[Isopsephy|summing up]] of all the [[Abjadi order|numerical values of each Arabic letter]] making up the phrase.<ref>{{cite book|pages=581, 587–8|title=The Oxford Handbook of Qur'anic Studies|editor1=Shah|editor2=Haleem|publisher=Oxford University Press|year=2020}}</ref> This auspiciousness has led it to often feature in films from the country.
* Vijay Verma's ([[Amitabh Bachchan]]) [[coolie]] number in the 1975 Hindi film ''[[Deewaar]]''.
** Raja's ([[Rajnikanth]]) coolie number in the 1981 Tamil film ''[[Thee (1981 film)|Thee]]'', a remake of ''Deewaar''.
* Iqbal Khan's ([[Amitabh Bachchan]]) coolie number in the 1983 Hindi film ''[[Coolie (1983 Hindi film)|Coolie]]''. 
** Bachchan has indicated that he believes the number is auspicious, as he survived a serious injury while wearing this number during the shooting of ''Coolie''.
* [[Chiranjeevi]] sported this number in the 1988 Telugu film [[Khaidi No.786]].
* Veer Pratap Singh's ([[Shah Rukh Khan|Shahrukh Khan]]) prisoner number in the 2004 Hindi film [[Veer-Zaara]].
* Sultan's ([[Ajay Devgan]]) car in the 2010 Hindi film [[Once Upon a Time in Mumbaai]] bears the registration number MRH 786.
* In the 2011 Tamil film [[Mankatha]], in the scene where Vinayak Mahadev ([[Ajith Kumar]]) shoots Prem ([[Premgi Amaren]]), Prem wears has a gold plate on his chest with the number 786 written on it.
* [[Ashish R Mohan]]'s 2012 Hindi film [[Khiladi 786]] features [[Akshay Kumar]] in the title role. The same film was released in Pakistan without the number 786.<ref>{{Cite news|url=http://timesofindia.indiatimes.com/entertainment/movie-reviews/hindi/Khiladi-786/movie-review/17504813.cms|title = Khiladi 786 Movie Review {3/5}: Critic Review of Khiladi 786 by Times of India|website = [[The Times of India]]}}</ref>

== References ==
{{reflist}}

==External links==
{{Commons category}}
*[http://www.e-786.com/4436/17601.html e-786.com Permissible to write 786]
*[https://web.archive.org/web/20051102071409/http://www.submission.org/miracle/786.html United Submitters analysis of 786]

{{Integers|7}}

[[Category:Integers]]