Editing 100 (section)

==In mathematics==
[[File:cube-sum-100.png|thumb|100 as the sum of the first positive cubes]]
100 is the square of [[10 (number)|10]] (in [[scientific notation]] it is written as 10<sup>2</sup>). The standard [[SI prefix]] for a hundred is "[[Hecto-|hecto]]-".

100 is the basis of [[percentage]]s ({{Lang|la|per centum}} meaning "by the hundred" in Latin), with 100% being a full amount.

100 is a [[Harshad number]] in [[decimal]], and also in base-four, a base in-which it is also a [[self-descriptive number]].<ref>{{Cite web|url=https://oeis.org/A005349|title=Sloane's A005349 : Niven (or Harshad) numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-27}}</ref><ref>{{Cite OEIS |A108551 |Self-descriptive numbers in various bases represented in base 10 |access-date=2022-12-08 }}</ref>

100 is the sum of the first nine [[prime number]]s, from [[2]] through [[23 (number)|23]].<ref>{{cite OEIS|A007504|Sum of the first n primes.}}</ref> It is also divisible by the number of primes below it, [[25 (number)|25]].<ref>{{cite OEIS|A057809|Numbers n such that pi(n) divides n.}}</ref>

100 cannot be expressed as the difference between any integer and the total of [[coprime]]s below it, making it a [[noncototient]].<ref>{{Cite OEIS |A005278 |Noncototients |access-date=2022-12-08 }}</ref>

100 has a [[Carmichael function|reduced totient]] of 20, and an [[Euler totient]] of 40.<ref>{{Cite OEIS |A002322 |Reduced totient function |access-date=2022-12-08 }}</ref><ref>{{Cite OEIS |A000010 |Euler totient function }}</ref> A totient value of 100 is obtained from four numbers: [[101 (number)|101]], [[125 (number)|125]], [[202 (number)|202]], and [[250 (number)|250]].

100 can be expressed as a sum of some of its divisors, making it a [[semiperfect number]].<ref>{{Cite OEIS |A005835 |Pseudoperfect (or semiperfect) numbers n |access-date=2022-12-08 }}</ref> The [[geometric mean]] of its nine divisors is [[10 (number)|10]].

100 is the sum of the [[Cube (algebra)|cubes]] of the first four positive [[integers]] (100 = 1<sup>3</sup> + 2<sup>3</sup> + 3<sup>3</sup> + 4<sup>3</sup>).<ref>{{Cite OEIS |A025403 |Numbers that are the sum of 4 positive cubes in exactly 1 way. |access-date=2022-12-08 }}</ref> This is related by [[Nicomachus's theorem]] to the fact that 100 also equals the square of the sum of the first four positive integers: {{nowrap|1=100 = 10<sup>2</sup> = (1 + 2 + 3 + 4)<sup>2</sup>}}.<ref>{{Cite OEIS|A000537|name=Sum of first n cubes; or n-th triangular number squared}}</ref>

100 = 2<sup>6</sup> + 6<sup>2</sup>, thus 100 is the seventh [[Leyland number]].<ref>{{Cite web|url=https://oeis.org/A076980|title=Sloane's A076980 : Leyland numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-27}}</ref> 100 is also the seventeenth [[Erdős–Woods number]], and the fourth 18-[[Polygonal number|gonal number]].<ref>{{Cite OEIS |A059756 |Erdős-Woods numbers: the length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints |access-date=2022-11-30 }}</ref><ref>{{Cite web|url=https://oeis.org/A051870|title=Sloane's A051870 : 18-gonal numbers|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-27}}</ref>

It is the 10th [[star number]]<ref>{{Cite OEIS |A003154 |access-date=2023-09-02 }}</ref> (whose [[digit sum]] also adds to 10 in [[Base ten|decimal]]).