28 (twenty-eight) is the natural number following 27 and preceding 29.
| ||||
---|---|---|---|---|
Cardinal | twenty-eight | |||
Ordinal | 28th (twenty-eighth) | |||
Factorization | 22 × 7 | |||
Divisors | 1, 2, 4, 7, 14, 28 | |||
Greek numeral | ΚΗ´ | |||
Roman numeral | XXVIII | |||
Binary | 111002 | |||
Ternary | 10013 | |||
Senary | 446 | |||
Octal | 348 | |||
Duodecimal | 2412 | |||
Hexadecimal | 1C16 |
It is a composite number; a square-prime, of the form (p2,q) where q is a higher prime. It is the third of this form and of the specific form (22.q), with proper divisors being 1, 2, 4, 7, and 14.
Twenty-eight is the second perfect number - it is the sum of its proper divisors: . As a perfect number, it is related to the Mersenne prime 7, since . The next perfect number is 496, the previous being 6.[1]
Though perfect, 28 is not the aliquot sum of any other number other than itself, and so; unusually, is not part of a multi-number aliquot sequence. The next perfect number is 496.
Twenty-eight is the sum of the totient function for the first nine integers.[2]
Since the greatest prime factor of is 157, which is more than 28 twice, 28 is a Størmer number.[3]
Twenty-eight is a harmonic divisor number,[4] a happy number,[5] a triangular number,[6] a hexagonal number,[7] a Leyland number of the second kind and a centered nonagonal number.[8]
It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).[9]
It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, 18, 28...[10]
There are twenty-eight convex uniform honeycombs.
Twenty-eight is the only positive integer that has a unique Kayles nim-value.
Twenty-eight is the only known number that can be expressed as a sum of the first nonnegative (or positive) integers ( ), a sum of the first primes ( ) and a sum of the first nonprimes ( ), and it is unlikely that any other number has this property.[11]
There are twenty-eight oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.[citation needed]
There are 28 elements of the cuboid: 8 vertices, 12 edges, 6 faces, 2 3-dimensional elements (interior and exterior).
There are 28 non-equivalent ways of expressing 1000 as the sum of two prime numbers[12]
The cube of 12 (1728 = 123) contains a total of twenty-eight divisors (the third-smallest number after 1344 and 960, and preceding 2112).
28 is the smallest number that can be expressed as the sum of four nonzero squares in (at least) three ways: , or (see image).[13][14]
Twenty-eight is: