38 (number)

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← 37 38 39 →
Cardinalthirty-eight
Ordinal38th
(thirty-eighth)
Factorization2 × 19
Divisors1, 2, 19, 38
Greek numeralΛΗ´
Roman numeralXXXVIII
Binary1001102
Ternary11023
Quaternary2124
Quinary1235
Senary1026
Octal468
Duodecimal3212
Hexadecimal2616
Vigesimal1I20
Base 361236

38 (thirty-eight) is the natural number following 37 and preceding 39.

In mathematics[edit]

  • 38! − 1 yields 523022617466601111760007224100074291199999999, which is the 16th factorial prime.[1]
  • There is no answer to the equation φ(x) = 38, making 38 a nontotient.[2]
  • 38 is the sum of the squares of the first three primes.
  • 37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.
  • 38 is the largest even number which cannot be written as the sum of two odd composite numbers.
  • There are only two normal magic hexagons, order 1 (which is trivial) and order 3. The sum of each row of an order 3 magic hexagon is 38.[3]

In science[edit]

Astronomy[edit]

In other fields[edit]

Most people will see the number 38, but people with red-green color blindness might see 88 instead.

Thirty-eight is also:

  • The 38th parallel north is the pre-Korean War boundary between North Korea and South Korea.
  • The number of slots on an American roulette wheel (0, 00, and 1 through 36; European roulette does not use the 00 slot and has only 37 slots)
  • The number of games that each team in a sports league with 20 teams that plays a full home-and-away schedule (with each team playing the others one time home and one time away) will play in a season. The most notable leagues that currently have a 38-game season are the top divisions of association football in England and Spain, respectively the Premier League and La Liga.
  • Bill C-38 legalized same-sex marriage in Canada
  • The number of years it took the Israelites to travel from Kadesh Barnea to the Zered valley in Deuteronomy.
  • A "38" is often the name for a snub nose .38 caliber revolver
  • The 38 class is the most famous class of steam locomotive used in New South Wales
  • The number of the French department Isère
  • The "over-38 rule" is a feature of the NBA salary cap that affects contracts of players who turn 38 during their deals.

References[edit]

  1. ^ Sloane, N. J. A. (ed.). "Sequence A002982 (Numbers n such that n! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
  2. ^ (sequence A005277 in the OEIS)
  3. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.