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{{One source|date=January 2025}}
{{Infobox number
{{Infobox number
| number = 363
| number = 363

| divisor = [[1 (number)|1]], [[3 (number)|3]], [[11 (number)|11]], [[33 (number)|33]], [[121 (number)|121]], 363
| divisor = [[1 (number)|1]], [[3 (number)|3]], [[11 (number)|11]], [[33 (number)|33]], [[121 (number)|121]], 363
}}
}}
'''363''', three hundred [and] sixty three, is the [[integer]] after 362 and before 364.
'''363''' ('''three hundred [and] sixty-three''') is the [[natural number]] following [[362 (number)|362]] and preceding [[364 (number)|364]].


==In mathematics==
==In mathematics==
⚫
* 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59)
* It is an odd, [[composite number|composite]], [[Positive number|positive]], [[real number|real]] integer, composed of a [[prime number|prime]] (3) and a prime squared (11<sup>2</sup>).
* It is an odd, [[composite number|composite]], [[Positive number|positive]], [[real number|real]] integer, composed of a [[prime number|prime]] (3) and a prime squared (11<sup>2</sup>).
⚫
* 363 is a [[deficient number]] and a [[perfect totient number]].
* The 363rd day in a year is 29 December (28 December in [[leap year]]s).
* 363 is a [[palindromic number]] in bases 3, 10, 11 and 32.
* 363 is a [[palindromic number]] in bases 3, 10, 11 and 32.
⚫
* Any subset of its digits is divisible by three.
* 363 is a [[repdigit]] (BB) in base 32.
* 363 is a [[repdigit]] (BB) in base 32.
* The [[Mertens function]] returns 0.<ref>{{cite web|title=Sloane's A028442 : Numbers n such that Mertens' function is zero|url=https://oeis.org/A028442|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-06-02}}</ref>
* 363 is a 122-gonal number.
⚫
* Any subset of its digits is divisible by three.
⚫
* 363 is a [[deficient number]].
⚫
* 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
* The [[Mertens function]] returns 0
* 363 is the sum of 5 consecutive powers of three (3 + 9 + 27 + 81 + 243) [[deficient number]].
* 363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).
⚫
* 363 can be expressed as the sum of three squares in four different ways: 11<sup>2</sup> + 11<sup>2</sup> + 11<sup>2</sup>, 5<sup>2</sup> + 7<sup>2</sup> + 17<sup>2</sup>, 1<sup>2</sup> + 1<sup>2</sup> + 19<sup>2</sup>, and 13<sup>2</sup> + 13<sup>2</sup> + 5<sup>2</sup>.
* 363 cubits is the solution given to [[Rhind Mathematical Papyrus]] question 50 - find the side length of an octagon with the same area as a circle 9 [[Ancient Egyptian units of measurement|khet]] in diameter [http://www.seshat.ch/home/rhind6.htm].
* 363 cubits is the solution given to [[Rhind Mathematical Papyrus]] question 50 – find the side length of an octagon with the same area as a circle 9 [[Ancient Egyptian units of measurement|khet]] in diameter [http://www.seshat.ch/home/rhind6.htm].
⚫
* 363 can be expressed as the sum of three squares four different ways: 11<sup>2</sup> + 11<sup>2</sup> + 11<sup>2</sup>, 5<sup>2</sup> + 7<sup>2</sup> + 17<sup>2</sup>, 1<sup>2</sup> + 1<sup>2</sup> + 19<sup>2</sup>, and 13<sup>2</sup> + 13<sup>2</sup> + 5<sup>2</sup>.

==In other fields==
* The years AD 363 (in base 35 written AD AD) and [[363 BC]] (in base 32 written BB BC).
* [[Food additive]] E363 is [[succinic acid]] a [[food acid]].
* [[363 Padua]] is a (probably typical Main Band) [[Asteroid]]
* 363 is attested in [[Egyptian mythology]]. In the [[Edfu]] texts for example it appears to be associated with [[Thoth]]
* [[USS Balch (DD-363)]] was a [[Porter-class destroyer]] in the [[United States Navy]].
* 363 is the number of communes of the [[Maine-et-Loire]] département in [[France]]
* 363 is the London ''Laburnum'' dialling code for [[Winchmore Hill]].
* [[Technetium]]'s first [[spectral line]] is at 363&nbsp;nm.
* The [[Saturn V]] rocket is 363 feet tall.
* In [[Unicode]] the [[macron]] ū is <nowiki>&amp;#363;</nowiki>
* In the [[2000 U.S. election]] [[George W. Bush]] won [[New Mexico]] by 363 votes, and [[Florida]] by 363 votes on the two corner [[Chad (paper)|chad]] standard.
* In May 1877 the famous 363 [[France|French]] deputies passed the vote of no confidence in the [[duc de Broglie]] - the [[Seize Mai]].
* The [[Erie Canal]] is 363 miles long.
* The two [[Sender Donebach]] at 363 m are the second tallest structures in [[Germany]].
* [[DARPA|Arpa]] [[mailing list]]s are dealt with in RFC 363
* [[Resource Reservation Protocol|RSVP]] is assigned port 363 see RFC 2205
* [[Naphthalene]] is dealt with in PIM (Poisons Information Monograph) 363
* Form 363 is the [[Companies House]] annual return filed in the [[United Kingdom]].
* The 363 Group is a consulting firm in [[Chicago]].<ref>[http://www.363group.com/]</ref>

==In numerology==
* 363 may be associated with the [[messiah]]
* Number 363 is a compilation of the vibrations and energies of number 3 and number 6, with number 3 appearing twice, amplifying its influences and attributes.
* Main Key: The Creative, Innovative.
* Number 3 resonates with courage, forgiveness, skills and talents, open-mindedness, manifestation and attainment, self-expression and communication, optimism and enthusiasm, growth and expansion. Number 3 also carries the vibrations of the Ascended Masters. The Ascended Masters help you to focus on the Divine spark within yourself and others, and assist with manifesting your desires. They are helping you to find peace, clarity and love within.
* Number 6 relates to love of home and family and domesticity, service to others and selflessness, responsibility and reliability, providing for the self and others. Number 6 also resonates with personal willpower, independence, initiative, action and overcoming obstacles.

==Products==
* The 363 is model of mid-size [[cruiser]].


==References==
==References==
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{{Integers|3}}
{{Integers|3}}


[[Category:Integers|363]]
[[Category:Integers]]


{{Num-stub}}

Latest revision as of 17:26, 1 January 2025

← 362 363 364 →
Cardinalthree hundred sixty-three
Ordinal363rd
(three hundred sixty-third)
Factorization3 × 112
Divisors1, 3, 11, 33, 121, 363
Greek numeralΤΞΓ´
Roman numeralCCCLXIII, ccclxiii
Binary1011010112
Ternary1111103
Senary14036
Octal5538
Duodecimal26312
Hexadecimal16B16

363 (three hundred [and] sixty-three) is the natural number following 362 and preceding 364.

In mathematics

[edit]
  • It is an odd, composite, positive, real integer, composed of a prime (3) and a prime squared (112).
  • 363 is a deficient number and a perfect totient number.
  • 363 is a palindromic number in bases 3, 10, 11 and 32.
  • 363 is a repdigit (BB) in base 32.
  • The Mertens function returns 0.[1]
  • Any subset of its digits is divisible by three.
  • 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
  • 363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).
  • 363 can be expressed as the sum of three squares in four different ways: 112 + 112 + 112, 52 + 72 + 172, 12 + 12 + 192, and 132 + 132 + 52.
  • 363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter [1].

References

[edit]
  1. ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.


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