| ||||
---|---|---|---|---|
Cardinal | twenty-seven | |||
Ordinal | 27th | |||
Factorization | 33 | |||
Divisors | 1, 3, 9, 27 | |||
Greek numeral | ΚΖ´ | |||
Roman numeral | XXVII | |||
Binary | 110112 | |||
Ternary | 10003 | |||
Senary | 436 | |||
Octal | 338 | |||
Duodecimal | 2312 | |||
Hexadecimal | 1B16 |
27 (twenty-seven; Roman numeral XXVII) is the natural number following 26 and preceding 28.
Twenty-seven is the cube of 3, or three tetrated , divisible by the number of prime numbers below it (nine).
The first non-trivial decagonal number is 27. [1]
27 has an aliquot sum of 13 [2] (the sixth prime number) in the aliquot sequence of only one composite number, rooted in the 13-aliquot tree. [3]
The sum of the first four composite numbers is , [4] while the sum of the first four prime numbers is , [5] with 7 the fourth indexed prime. [6] [lower-alpha 1]
In the Collatz conjecture (i.e. the problem), a starting value of 27 requires 3 × 37 = 111 steps to reach 1, more than any smaller number. [10] [lower-alpha 2]
27 is also the fourth perfect totient number — as are all powers of 3 — with its adjacent members 15 and 39 adding to twice 27. [13] [lower-alpha 3]
A prime reciprocal magic square based on multiples of in a square has a magic constant of 27.
Including the null-motif, there are 27 distinct hypergraph motifs. [14]
There are exactly twenty-seven straight lines on a smooth cubic surface, [15] which give a basis of the fundamental representation of Lie algebra . [16] [17]
The unique simple formally real Jordan algebra, the exceptional Jordan algebra of self-adjoint 3 by 3 matrices of quaternions, is 27-dimensional; [18] its automorphism group is the 52-dimensional exceptional Lie algebra [19]
There are twenty-seven sporadic groups, if the non-strict group of Lie type (with an irreducible representation that is twice that of in 104 dimensions) [20] is included. [21]
In Robin's theorem for the Riemann hypothesis, twenty-seven integers fail to hold for values where is the Euler–Mascheroni constant; this hypothesis is true if and only if this inequality holds for every larger [22] [23] [24]
In decimal, 27 is the first composite number not divisible by any of its digits, as well as:
Also in base ten, if one cyclically rotates the digits of a three-digit number that is a multiple of 27, the new number is also a multiple of 27. For example, 378, 783, and 837 are all divisible by 27.
In senary (base six), one can readily test for divisibility by 43 (decimal 27) by seeing if the last three digits of the number match 000, 043, 130, 213, 300, 343, 430, or 513.
In decimal representation, 27 is located at the twenty-eighth (and twenty-ninth) digit after the decimal point in π:
If one starts counting with zero, 27 is the second self-locating string after 6, of only a few known. [27] [28]
Twenty-seven is also:
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.
10 (ten) is the even natural number following 9 and preceding 11. Ten is the base of the decimal numeral system, the most common system of denoting numbers in both spoken and written language.
21 (twenty-one) is the natural number following 20 and preceding 22.
45 (forty-five) is the natural number following 44 and preceding 46.
90 (ninety) is the natural number following 89 and preceding 91.
25 (twenty-five) is the natural number following 24 and preceding 26.
84 (eighty-four) is the natural number following 83 and preceding 85.
32 (thirty-two) is the natural number following 31 and preceding 33.
37 (thirty-seven) is the natural number following 36 and preceding 38.
55 (fifty-five) is the natural number following 54 and preceding 56.
57 (fifty-seven) is the natural number following 56 and preceding 58.
58 (fifty-eight) is the natural number following 57 and preceding 59.
63 (sixty-three) is the natural number following 62 and preceding 64.
144 is the natural number following 143 and preceding 145.
135 is the natural number following 134 and preceding 136.
138 is the natural number following 137 and preceding 139.
240 is the natural number following 239 and preceding 241.
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered attention throughout history in part because distal extremities in humans typically contain five digits.
744 is the natural number following 743 and preceding 745.
888 is the natural number following 887 and preceding 889.
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: CS1 maint: Zbl (link)Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987), p. 106.