View source for 100,000,000,000,000

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{{Infobox number
| number        = 100000000000000
| cardinal      = Hundred trillion ([[long and short scales|short scale]])<br/>Hundred billion ([[long and short scales|long scale]])<br/>Hundred thousand billion<br/>Hundred million million
| ordinal       = 100000000000000th (hundred trillionth, short scale)
| factorization = {{hlist|2<sup>14</sup>|5<sup>14</sup>}}
| divisor       = 225 total
}}
{{Portal|Mathematics}}
'''100,000,000,000,000''' ('''hundred trillion''' on the short scale; '''hundred billion''' on the long scale; hundred thousand [[1,000,000,000|billion]]; hundred million [[1,000,000|million]]) is the [[natural number]] following [[10,000,000,000,000#99,000,000,000,000 to 99,999,999,999,999|99,999,999,999,999]] and preceding 100,000,000,000,001. It is known as 1 [[lakh]] arab, 1000 kharab, 1 crore [[crore]], or 10 nil in the Indian numbering system.

== Properties and usage ==
100,000,000,000,000 has the following properties and usage:
=== In mathematics ===
*It is [[Even number|even]], [[Composite number|composite]], [[Abundant number|abundant]], [[Polite number|polite]], [[Practical number|practical]], [[Frugal number|frugal]], and [[Regular number|regular]]. It is also a [[perfect power]] and a [[harshad number]].
*It is written in scientific notation as '''1 × 10<sup>14</sup>''' or '''10<sup>14</sup>''' ('''1E+14''' or simply '''1E14''' in [[Scientific notation#E notation|E notation]]).
*It has a total of 225 divisors (210 even, 15 odd). All divisors are displayed below:
<blockquote><small>1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000, 10240, 12500, 12800, 15625, 16000, 16384, 20000, 20480, 25000, 25600, 31250, 32000, 40000, 40960, 50000, 51200, 62500, 64000, 78125, 80000, 81920, 100000, 102400, 125000, 128000, 156250, 160000, 200000, 204800, 250000, 256000, 312500, 320000, 390625, 400000, 409600, 500000, 512000, 625000, 640000, 781250, 800000, 1000000, 1024000, 1250000, 1280000, 1562500, 1600000, 1953125, 2000000, 2048000, 2500000, 2560000, 3125000, 3200000, 3906250, 4000000, 5000000, 5120000, 6250000, 6400000, 7812500, 8000000, 9765625, 10000000, 10240000, 12500000, 12800000, 15625000, 16000000, 19531250, 20000000, 25000000, 25600000, 31250000, 32000000, 39062500, 40000000, 48828125, 50000000, 51200000, 62500000, 64000000, 78125000, 80000000, 97656250, 100000000, 125000000, 128000000, 156250000, 160000000, 195312500, 200000000, 244140625, 250000000, 256000000, 312500000, 320000000, 390625000, 400000000, 488281250, 500000000, 625000000, 640000000, 781250000, 800000000, 976562500, 1000000000, 1220703125, 1250000000, 1280000000, 1562500000, 1600000000, 1953125000, 2000000000, 2441406250, 2500000000, 3125000000, 3200000000, 3906250000, 4000000000, 4882812500, 5000000000, 6103515625, 6250000000, 6400000000, 7812500000, 8000000000, 9765625000, 10000000000, 12207031250, 12500000000, 15625000000, 16000000000, 19531250000, 20000000000, 24414062500, 25000000000, 31250000000, 32000000000, 39062500000, 40000000000, 48828125000, 50000000000, 62500000000, 78125000000, 80000000000, 97656250000, 100000000000, 125000000000, 156250000000, 160000000000, 195312500000, 200000000000, 250000000000, 312500000000, 390625000000, 400000000000, 500000000000, 625000000000, 781250000000, 800000000000, 1000000000000, 1250000000000, 1562500000000, 2000000000000, 2500000000000, 3125000000000, 4000000000000, 5000000000000, 6250000000000, 10000000000000, 12500000000000, 20000000000000, 25000000000000, 50000000000000, 100000000000000</small></blockquote>
*The sum of all its divisors, including itself, is 249,992,370,597,277.
*It has an [[Euler's totient function|Euler totient]] of 40,000,000,000,000, and an [[aliquot sum]] of 149,992,370,597,277.
*There are a total of 3,204,941,750,802 positive [[prime number|prime]]s less than it.<ref name=A006880>{{Cite OEIS|A006880|Number of primes less than 10^n}}</ref>
*Below is the list of basic calculations of 100,000,000,000,000:
{| class="wikitable" style="margin:1em auto; text-align: center; background: white"
! style="width:50px;" |
! style="width:150px;" |[[Multiplication]]<br/><math>\scriptstyle{\text{100,000,000,000,000 }\times\text{ x}}</math>
! style="width:150px;" |[[Division (mathematics)|Division]]<br/><math>\scriptstyle{\text{100,000,000,000,000 }\div\text{ x}}</math>
! style="width:150px;" |[[Exponentiation]]<br/><math>\scriptstyle{\text{100,000,000,000,000}^\text{x}}</math>
! style="width:150px;" |[[nth root|{{mvar|n}}th root]]<br/>
<math>\scriptstyle{\sqrt[\text{x}]{\text{100,000,000,000,000}}}</math>
|-
|2||200,000,000,000,000||50,000,000,000,000||10<sup>28</sup>||10,000,000
|-
|3||300,000,000,000,000||33,333,333,333,333.{{overline|3}}||10<sup>42</sup>||≈46,415.8883
|-
|4||400,000,000,000,000||25,000,000,000,000||10<sup>56</sup>||≈3,162.2776
|-
|5||500,000,000,000,000||20,000,000,000,000||10<sup>70</sup>||≈630.9573
|-
|6||600,000,000,000,000||16,666,666,666,666.{{overline|6}}||10<sup>84</sup>||≈215.4434
|-
|7||700,000,000,000,000||14,285,714,285,714.{{overline|285714}}||10<sup>98</sup>||100
|-
|8||800,000,000,000,000||12,500,000,000,000||10<sup>112</sup>||≈56.2341
|-
|9||900,000,000,000,000||11,111,111,111,111.{{overline|1}}||10<sup>126</sup>||≈35.9381
|-
|10||1,000,000,000,000,000||10,000,000,000,000||10<sup>140</sup>||≈25.1188
|}

== Selected 15-digit numbers (100,000,000,000,001–999,999,999,999,999) ==
=== 100,000,000,000,001 to 199,999,999,999,999 ===
*'''100,000,000,000,031''' : smallest 15-digit [[prime number]]<ref name="A003617">{{Cite OEIS|A003617|Smallest n-digit prime}}</ref>
*'''100,000,012,392,316''' : smallest 15-digit [[triangular number]], 14,142,136th triangular number<ref name="A068093">{{Cite OEIS|A068093|Smallest n-digit triangular number}}</ref><ref name="A068092">{{Cite OEIS|A068092|Index of smallest triangular number with n digits}}</ref>
*'''100,169,256,075,517''' : 202nd [[Markov number]]<ref name="A002559">{{Cite OEIS|A002559|Markoff (or Markov) numbers}}</ref>
*'''106,974,698,806,081''' : 203rd Markov number
*'''111,111,111,111,111''' : [[repunit]]
*'''111,146,809,165,122''' : 43rd [[Wedderburn-Etherington number]]<ref name="A001190">{{Cite OEIS|A001190|Wedderburn-Etherington numbers}}</ref>
*'''114,988,706,524,270''' : 34th [[Motzkin number]]<ref name="A001006">{{Cite OEIS|A001006|Motzkin numbers}}</ref>
*'''117,669,030,460,994''' : 204th Markov number, 69th [[Fibonacci number]]
*'''120,984,833,091,531''' : 53rd [[repfigit]]<ref name=A007629>{{Cite OEIS|A007629|
Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)}}</ref>
*'''124,145,519,261,542''' : 38th [[Pell number]]<ref name="A000129">{{Cite OEIS|A000129|Pell numbers}}</ref>
*'''124,738,635,483,875''' : number of series-reduced planted trees with 51 nodes<ref name="A001678">{{Cite OEIS|A001678|Number of series-reduced planted trees with n nodes}}</ref>
*'''127,353,146,734,466''' : 205th Markov number
*'''130,429,015,516,800''' : 82nd [[superabundant number]]<ref name="A004394">{{Cite OEIS|A004394|
Superabundant [or super-abundant] numbers}}</ref>
*'''144,403,552,893,600''' : 83rd superabundant number
*'''145,624,636,022,689''' : 206th Markov number
*'''148,135,740,183,017''' : 207th Markov number
*'''151,620,880,341,401''' : 208th Markov number
*'''152,657,555,033,144''' : number of (unordered, unlabeled) rooted trimmed [[Tree (graph theory)|trees]] with 41 nodes<ref name="A002955">{{Cite OEIS|A002955|Number of (unordered, unlabeled) rooted trimmed trees with n nodes}}</ref>
*'''163,767,326,286,012''' : number of 55-bead necklaces (turning over is allowed) where complements are equivalent<ref name="A000011">{{Cite OEIS|A000011|Number of n-bead necklaces (turning over is allowed) where complements are equivalent}}</ref>
*'''166,799,988,689,300''' : number of 54-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed<ref name="A000013">{{Cite OEIS|A000013|Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed}}</ref>
*'''180,995,342,924,521''' : 209th Markov number
*'''184,717,953,466,367''' : 42nd [[Woodall number]]<ref name="A003261">{{Cite OEIS|A003261|Woodall (or Riesel) numbers}}</ref>
*'''187,611,224,490,881''' : 210th Markov number
*'''190,392,490,709,135''' : 70th Fibonacci number
*'''195,643,523,275,200''' : 84th superabundant number, 20th [[superior highly composite number]]<ref name=A002201>{{Cite OEIS|A002201|Superior highly composite numbers}}</ref>
=== 200,000,000,000,000 to 299,999,999,999,999 ===
*'''213,458,046,676,875''' = 27[[double factorial|!!]]
*'''215,440,028,338,359''' : number of secondary structures of RNA molecules with 40 nucleotides<ref name=A004148>{{Cite OEIS|A004148|Generalized Catalan numbers}}</ref>
*'''217,774,440,785,026''' : 211th Markov number
*'''222,222,222,222,222''' : [[repdigit]]
*'''238,763,690,000,642''' : 212th Markov number
*'''259,215,937,709,463''' : 22nd [[Schröder–Hipparchus number]]<ref name="A001003">{{Cite OEIS|A001003|Schroeder's second problem (generalized parentheses)}}</ref>
*'''259,918,212,890,625''' : 27th [[automorphic number]]<ref name="A003226">{{Cite OEIS|A003226|Automorphic numbers}}</ref>
*'''262,229,286,072,101''' : 213th Markov number
*'''263,747,951,750,360''' : 28th [[Catalan number]]<ref name="A000108">{{Cite OEIS|A000108|Catalan numbers}}</ref>
*'''265,077,991,831,995''' : number of series-reduced planted trees with 52 nodes
*'''266,552,682,265,118''' : 44th Wedderburn-Etherington number
*'''270,585,509,032,586''' : 54th repfigit
*'''288,807,105,787,200''' : 85th superabundant number
*'''299,713,796,309,065''' : 214th Markov number, 39th Pell number
=== 300,000,000,000,000 to 399,999,999,999,999 ===
*'''308,061,521,170,129''' : 215th Markov number, 71st Fibonacci number
*'''316,141,040,381,993''' : 216th Markov number
*'''321,685,824,284,100''' : number of 56-bead necklaces (turning over is allowed) where complements are equivalent
*'''327,534,518,354,296''' : number of 55-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
*'''330,931,069,469,828''' : 35th Motzkin number
*'''332,380,318,337,465''' : 217th Markov number
*'''333,333,333,333,333''' : repdigit
*'''335,990,918,918,981''' : 17th [[alternating factorial]]<ref>{{cite OEIS|A005165|Alternating factorials}}</ref>
*'''355,687,428,096,000''' = 17[[factorial|!]]
*'''355,687,428,096,153''' : 17th [[factoriangular number]]<ref name="A101292">{{Cite OEIS|A101292}}</ref>
*'''378,231,999,954,943''' : 43rd Woodall number
*'''379,325,837,704,445''' : 218th Markov number
*'''381,249,713,544,034''' : 219th Markov number
*'''382,745,902,953,654''' : number of (unordered, unlabeled) rooted trimmed trees with 42 nodes
=== 400,000,000,000,000 to 499,999,999,999,999 ===
*'''426,776,599,819,081''' : 220th Markov number
*'''433,210,658,680,800''' : 86th superabundant number
*'''444,444,444,444,444''' : repdigit
*'''459,789,046,174,429''' : 221st Markov number
*'''473,638,416,248,177''' : 222nd Markov number
*'''498,454,011,879,264''' : 72nd Fibonacci number
=== 500,000,000,000,000 to 599,999,999,999,999 ===
*'''542,557,456,311,485''' : 223rd Markov number
*'''544,288,586,926,914''' : number of secondary structures of RNA molecules with 41 nucleotides
*'''554,510,738,235,029''' : 224th Markov number
*'''555,555,555,555,555''' : repdigit
*'''563,637,117,190,957''' : number of series-reduced planted trees with 53 nodes
*'''577,614,211,574,400''' : 87th superabundant number
=== 600,000,000,000,000 to 699,999,999,999,999 ===
*'''632,084,292,449,766''' : number of 57-bead necklaces (turning over is allowed) where complements are equivalent
*'''639,754,054,803,187''' : 45th Wedderburn-Etherington number
*'''643,371,380,132,744''' : number of 56-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed
*'''666,666,666,666,666''' : repdigit
*'''668,746,232,531,714''' : 225th Markov number
*'''686,480,075,504,546''' : 226th Markov number
=== 700,000,000,000,000 to 799,999,999,999,999 ===
*'''723,573,111,879,672''' : 40th Pell number
*'''740,081,787,109,376''' : 28th automorphic number
*'''754,788,753,590,897''' : 55th repfigit
*'''767,465,181,141,553''' : 227th Markov number
*'''774,056,185,954,303''' : 44th Woodall number
*'''777,777,777,777,777''' : repdigit
=== 800,000,000,000,000 to 899,999,999,999,999 ===
*'''806,515,533,049,393''' : 228th Markov number, 73rd Fibonacci number
*'''866,421,317,361,600''' : 88th superabundant number
*'''867,493,136,119,153''' : 229th Markov number
*'''888,888,888,888,888''' : repdigit
=== 900,000,000,000,000 to 999,999,999,999,999 ===
*'''953,467,954,114,363''' : 36th Motzkin number, largest known Motzkin prime
*'''960,445,232,762,244''' : number of (unordered, unlabeled) rooted trimmed trees with 43 nodes
*'''971,341,527,703,714''' : 230th Markov number
*'''998,123,312,425,769''' : 231st Markov number
*'''999,999,999,999,989''' : largest 15-digit prime number<ref name="A003618">{{Cite OEIS|A003618|Largest n-digit prime}}</ref>
*'''999,999,999,999,999''' : largest 15-digit number, repdigit

== See also ==
*[[Long and short scales]]
*[[Names of large numbers]]
*[[Orders of magnitude (numbers)]]
*[[Power of 10]]

== References ==
<!-- See https://en.wikipedia.org/wiki/Help:Referencing_for_beginners on how to create references. -->
{{Reflist}}

{{Large numbers}}
{{Integers|10}}
{{Portal bar|Mathematics}}

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[[:Category:Large numbers]]
[[:Category:Powers of ten]]