38 (number)

This article discusses the number thirty-eight. For the year 38 CE, see 38. For other uses of 38, see 38 (disambiguation)

← 37 39 → 38
← 30 31 32 33 34 35 36 37 38 39 → List of numbers — Integers 0 10 20 30 40 50 60 70 80 90 →
Cardinal	thirty-eight
Ordinal	38th (thirty-eighth)
Factorization	$2 \cdot 19$
Divisors	1, 2, 19, 38
Roman numeral	XXXVIII
Binary	1001102
Octal	468
Duodecimal	3212
Hexadecimal	2616

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

In mathematics

38 is the 11th distinct semiprime and the 7th in the {2.q} family. It is the initial member of the third distinct semiprime pair (38, 39).

38 has an aliquot sum of 22 which is itself a distinct semiprime In fact 38 is the first number to be at the head of a chain of four distinct semiprimes in its 8 member aliquot sequence (38, 22, 14, 10, 8, 7, 1, 0). 38 is the 8th member of the 7-aliquot tree.

38! - 1 yields 523022617466601111760007224100074291199999999, which is a factorial prime.

There is no answer to the equation φ(x) = 38, making 38 a nontotient.^[1]

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.^[2]

In science

• The atomic number of strontium

Astronomy

• The Messier object M38, a magnitude 7.0 open cluster in the constellation Auriga
• The Saros number of
  • the solar eclipse series which began on -1729 June 26 and ended on -431 August 14. The duration of Saros series 38 was 1298.1 years, and it contained 73 solar eclipses.
  • the lunar eclipse series which began on -1408 April 16 and ended on -111 June 3. The duration of Saros series 38 was 1298.1 years, and it contained 73 lunar eclipses.
• The New General Catalogue object NGC 38, a spiral galaxy in the constellation Pisces
• The 38th parallel north is pre-Korean War boundary between North Korea and South Korea.

In mythology

• The number 38 was especially prominent in Norse mythology. The number was said to represent unnatural bravery, characteristic of the legendary heroes of Norse sagas. Most legendary sagas were divided into 38 chapters, and the number often recurred throughout stories, with the heroes combating giants or other beasts in groups of 38. The number came to be adopted by the Hardrada clan, and was displayed on their crest in the form of 38 ravens set around 38 outward-facing arrows.^{[citation needed]}
• The number was also significant in Egyptian mythology, as it was the characteristic number of Anubis, the jackal-headed god of death and mummification. Egyptian pharaohs were often buried with 38 statues of cat guardians, and their sarcophagi were adorned with 38 ankhs.

In other fields

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

Thirty-eight is also:

• 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 the current English Premiership, the top division in English Association Football, plays in a season
• 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
• Name of the southern rock band 38 Special
• The 38 class is the most famous class of steam locomotive used in New South Wales
• The number of the French department Isère
• There are 38 surviving plays written by William Shakespeare.
• The gate of the sci-fi TV series Stargate SG-1 can stay open a maximum of 38 minutes.
• In Taiwan, "3, 8", but not "38", is slang for stupid/idiot.

Historical years

38 A.D., 38 B.C., 1938 A.D., 2038, etc.

References

1. ^ (sequence A005277 in OEIS)
2. ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.