228 (two hundred
ndtwenty-eight) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called '' cardinal ...
following
227
Year 227 ( CCXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Senecio and Fulvius (or, less frequently, year 980 ''Ab urbe condi ...
and preceding
229
__NOTOC__
Year 229 (Roman numerals, CCXXIX) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Cassius (or, less frequentl ...
.
In mathematics
228 is a
refactorable number
A refactorable number or tau number is an integer ''n'' that is divisible by the count of its divisors, or to put it algebraically, ''n'' is such that \tau(n)\mid n. The first few refactorable numbers are listed in as
: 1, 2, 8, 9, 12, 18, ...
and a
practical number
In number theory, a practical number or panarithmic number is a positive integer n such that all smaller positive integers can be represented as sums of distinct divisors of n. For example, 12 is a practical number because all the numbers from 1 ...
.
There are 228
matchings in a
ladder graph
In the mathematical field of graph theory, the ladder graph is a planar, undirected graph with vertices and edges.
The ladder graph can be obtained as the Cartesian product of two path graphs, one of which has only one edge: .
Properties
B ...
with five rungs.
228 is the smallest even number ''n'' such that the numerator of the ''n''th
Bernoulli number
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, ...
is divisible by a nontrivial
square number
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as .
The u ...
that is
relatively prime
In mathematics, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivale ...
to ''n''.
The binary form of 228 contains all the two digit binary numbers in sequence from highest to lowest (11 10 01 00).
References
Integers
{{Num-stub