38 (number)

← 37 38 39 →
← 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 × 19
Divisors	1, 2, 19, 38
Roman numeral	XXXVIII
Binary	1001102
Ternary	11023
Quaternary	2124
Quinary	1235
Senary	1026
Octal	468
Duodecimal	3212
Hexadecimal	2616
Vigesimal	1I20
Base 36	1236

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 the 16th 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

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 38th parallel north is 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 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
• The 38 class is the most famous class of steam locomotive used in New South Wales
• The number of the French department Isère
• The number of Bach flower remedies.

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.