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# 38 (number)

 ← 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
Vigesimal1I20
Base 361236

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:

## References

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.
This page was last edited on 21 July 2019, at 21:07
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