# 38 (number)

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

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

## In mathematics

• 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 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 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.