270 (two hundred
ndseventy) 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 n ...
following
269 and preceding
271
__NOTOC__
Year 271 ( CCLXXI) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Aurelianus and Bassus (or, less frequently, year 1024 '' ...
.
In mathematics
*270 is a
harmonic divisor number
In mathematics, a harmonic divisor number, or Ore number (named after Øystein Ore who defined it in 1948), is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers are:
: 1, 6, 2 ...
*270 is the fourth number that is divisible by its average integer divisor
*270 is 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 ...
, by the second definition
*The sum of the
coprime
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 ...
counts for the first 29 integers is 270
*270 is a
sparsely totient number In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, ''n'', is sparsely totient if for all ''m'' > ''n'',
:\varphi(m)>\varphi(n)
where \varphi is Euler's totient function. The first few sparsely totien ...
, the largest integer with 72 as its totient
*Given 6 elements, there are 270 square permutations
*10! has 270
divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...
s
*270 is a
Harshad number
In mathematics, a harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written in that base.
Harshad numbers in base are also known as -harshad (or -Niven) numbers.
Harshad numbers ...
in base 10
*270 is the smallest positive integer that has divisors ending by digits 1, 2, ..., 9.
*270 is the smallest sum of a set of even numbers that contain every digit once.
In other fields
*The year
270 BC
*The year
270 AD
*The caliber of the
.270 Winchester
The .270 Winchester is a rifle cartridge developed by Winchester Repeating Arms Company in 1923 and unveiled in 1925 as a chambering for their bolt-action Model 54The Complete Reloading Manual for the .270 Winchester, Loadbooks USA, Inc., 2004 ...
rifle
*The number of
U.S. Electoral College
The United States Electoral College is the group of presidential electors required by the Constitution to form every four years for the sole purpose of appointing the president and vice president. Each state and the District of Columbia appo ...
votes needed to be elected President of the United States
*The average number of days in human pregnancy
Integers from 271 to 279
271
272
272 = 2
4·17, sum of four consecutive primes (61 + 67 + 71 + 73)
Euler number primitive semiperfect number, pronic number. 272 is the smallest palindrome divisible by a fourth power.
273
274
274 = 2·137, tribonacci number, Smith number, nontotient, noncototient, centered triangular number, oeis:A006316, 274
64 + 1 is prime
275
275 = 5
2·11. 275 is the sum of fifth powers of the first two primes. The maximal number of pieces that can be obtained by cutting an annulus with 22 cuts.
276
277
278
278 = 2·139 = Φ(30),
nontotient. 278 is the smallest semiprime such that the next semiprime (287) is its anagram.
279
279 = 3
2·31. Every positive integer is the sum of at most 279 eighth powers. See Waring's problem.
References
{{Integers, 2
Integers