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30 (number) - Wikipedia

From Wikipedia, the free encyclopedia

Natural number

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

30 is a square pyramidal number.

30 is an even, composite, and pronic number. With 2, 3, and 5 as its prime factors, it is a regular number and the first sphenic number, the smallest of the form 2 × 3 × r {\displaystyle 2\times 3\times r} , where r is a prime greater than 3. It has an aliquot sum of 42; within an aliquot sequence of thirteen composite numbers (30, 42, 54, 66, 78, 90, 144, 259, 45, 33, 15, 9, 4, 3, 1, 0) to the Prime in the 3-aliquot tree. From 1 to the number 30, this is the longest Aliquot Sequence.

It is also:

Furthermore,

In a group G, such that | G | = p n × m {\displaystyle |G|=p^{n}\times m} , where p does not divide m, and has a subgroup of order p n {\displaystyle p^{n}} , 30 is the only number less than 60 that is neither a prime nor of the aforementioned form. Therefore, 30 is the only candidate for the order of a simple group less than 60, in which one needs other methods to specifically reject to eventually deduce said order.[citation needed]

The SI prefix for 1030 is Quetta- (Q), and for 10−30 (i.e., the reciprocal of 1030) quecto (q). These numbers are the largest and smallest number to receive an SI prefix to date.

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