30 (number)

For other uses, see The Thirty.
29 30 31
Cardinal thirty
Ordinal 30th
(thirtieth)
Numeral system trigesimal
Factorization 2 × 3 × 5
Divisors 1, 2, 3, 5, 6, 10, 15, 30
Roman numeral XXX
Binary 111102
Ternary 10103
Quaternary 1324
Quinary 1105
Senary 506
Octal 368
Duodecimal 2612
Hexadecimal 1E16
Vigesimal 1A20
Base 36 U36

30 (thirty) is the natural number following 29 and preceding 31.

In mathematics

30 is the sum of the first four squares, which makes it a square pyramidal number.

It is a primorial and is the smallest Giuga number.

30 is the smallest sphenic number, and the smallest of the form 2 × 3 × r, where r is a prime greater than 3. 30 has an aliquot sum of 42; the second sphenic number and all sphenic numbers of this form have an aliquot sum 12 greater than themselves. The aliquot sequence of 30 is 16 members long, it comprises (30,42,54,66,78,90,144,259,45,33,15,9,4,3,1,0)

Thirty has but one number for which it is the aliquot sum:[1] the square number 841.[2]

Adding up some subsets of its divisors (e.g., 5, 10 and 15) gives 30, hence 30 is a semiperfect number.

30 is the largest number such that all coprimes smaller than itself, except for 1, are prime.[3]

A polygon with thirty sides is called a triacontagon.

The icosahedron and the dodecahedron are Platonic solids with 30 edges. The icosidodecahedron is an Archimedean solid with 30 vertices, and the Tutte–Coxeter graph is a symmetric graph with 30 vertices.

E8 has Coxeter number 30.

30 is a Harshad number.

Since any group G such that |G| = pnm, where p does not divide m, has a subgroup of order pn, and 30 is the only number less than 60 that is not either a prime or of the above form, it is the only candidate for the order of a simple group less than 60 that one needs other methods to reject.

Look up thirty in Wiktionary, the free dictionary.

In science

Astronomy

In other fields

Thirty is:

History and literature

Sports

Music

References

  1. "Sloane's A057709 : Numbers n such that there is a unique x for which the sum of the aliquot parts of x", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  2. "Sloane's A070015 : Least m such that sum of aliquot parts of m equals n", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
  3. Michael Slone, Every positive integer greater than 30 has at least one composite totative from PlanetMath. Accessed 24 April 2007
  4. Report of the 7 July Review Committee Accessed 18 Dec 2011
  5. Texas Rangers Retired Number History on mlb.com Retrieved May 18, 2006. Note however that Jackie Robinson's number 42 was retired by Major League Baseball for all teams.
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