How many trailing zeros are in 4096 factorial?

There are 1021 trailing zeros in 4096!. This is calculated using Legendre's formula: count how many times 5 divides into 4096, then 25, then 125, and so on, adding up all the quotients.

What is Legendre's formula?

Legendre's formula calculates the number of trailing zeros in n! by summing floor(n/5) + floor(n/25) + floor(n/125) + ... until the quotient becomes 0. Each trailing zero comes from a factor of 10, which requires one factor of 2 and one factor of 5.

Trailing zeros in 4096 factorial = 1021

Quick Answer: 1,021 trailing zeros in 4096!
Legendre's Formula: Count factors of 5 in 4096! ⌊4096/5⌋ = 819 + ⌊4096/25⌋ = 163 + ⌊4096/125⌋ = 32 + ⌊4096/625⌋ = 6 + ⌊4096/3125⌋ = 1 = 1021

Factorial Calculator Until 10,000

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Trailing Zeros in 4096!

Trailing zeros in 4096! = 1,021

How 4096! is calculated

The number of trailing zeros in 4096! is 1021.
The number of digits in 4096 factorial is 13020.
In scientific notation: 4096! ≈ 3.642736 × 10¹³⁰¹⁹
The factorial of 4096 is calculated, through its definition, this way:
4096! = 4096 • 4095 • 4094 • 4093 • 4092 ... 3 • 2 • 1

Exact value of 4096!

4096! = 36427363894570419315658274703116469205712449235098554299509384847803787493583241387491138852260192414089162355975180441627205998905094740308390559314460714086478086556387708301685874429122262002873651835914388507747682823605281121522657797736690000348651608440700612480475773480267025200325557327190940507040548909593911164433288212729920687676754028782714334413913174097205635382615469711531209207104887512360271750820233149035678050047954536544090561291694863670587872515754423200342792488252348768805395319432883529821703643874598322607248617240107308643234077839152872443674376344680168556883326373863958049769348649991349895178910490897544145740975708758346344807711256305886237161890094016363305364699379880585861641517781619567282556771670461458396978625340803923658485435690864317795307693130102720162164026599166042611151950196893112267960939492845839807810011344222861314390416395627472289943227918238117580143172943623664778882805483013877510556402850353420621304618166063968659568963028664159819485546116512196074650312777859190864535253697646914221190439078208345723015514900232490211449669445304030164511415608503840571387174525216318101241411784733092415770606466122348631473332743165155479655672025874105055481263874005459632091967813525715716589693170433308548237158060168601798239921062509485140759676999941304914726642121522117853884453970956864055502349087487927761994295569654129303319714870345047721171336924215772641151792738859061623728613712013704292298845400304784983376067301622317024839844784260626059272217449005535883839212582999121483644988916285631029419711999751502881943179452543718092338181644298378930670388563857434306504439572867011371635599296477673657497119956820548092843105219329374948917715686242722381628725473399737282871555676309574425452170828672424055501373389903877982683044205234420875335795288797702181503367695946123143490504451949797844688378560379172070932031166288568104169400035549594096556664002145950937081519805957187866300267500791409139510557942938821063242057793187132912016881994807537549168956483672965229553667546806013780633218260457363147094605620861296822434423389899483647144554802377167408804729511685301456207269502373553415059012382982902317532039089848971461619107915250016014831236238538654814899946923963025958868571594014445821550154089646981603340093182026201745345757631365825890562955665695866249766545433291955103886898326762989686539642896967252134101348149659861882396078589729190590763694129472511800329277218837263294996066415850331313644806862951193592965131296997113366140964904012852575902916612909808769287250462809967081649869226486466207343357168976835115081023710074968491481787167965221695061227123235540313408515421598762783465929494885178836710509866954865724866004551575213456976536284621279628440982280421009388709727106261888628088781019195673954735697473947722487596158018686154982482419695858939422024900209885159067617865779893803821512696543916293316402245896260653418982702638652755957965204542075308648066695506045939594976680223851292939673988282724477721580721728660575476199302746460606079340924831948868825984164049363959026470761061838128576238203270311047899093902373083298363898904195897388277593647692030142804774470756161482439444287197639688308263084311048740281453764679122813089504651504591439196427559223114960177985321750434628549932134693004133674787596298102285892494615600602248044542843606290903098335417082646069041169972666924549725975639611641864825702539295044199173815566428046422867221962644016105093873894960077314504454786024326205903555792821201896645251395145406733590937151664875034296947590438533439511479884543864865207058930659173544882375093534756572295436511305226235942518314914651560658628855280859475522866294013780232652246088796742744410487823989893404158496399762630218988806797367623020169056163562895907404607399186021943145098762844103652664444215328246767771938412481175164652554717274679537237769976583826971513970992642032407164499400269587370601101008414035841791363153469820670961469421309100374885051917475421991193515227483095060948624012247727494994817536132580396589366875647699919847739356948398356858801556893888992541040897907895478043405927378566892901025360707243230429385406619801104808343128821954045142916708309679739365611487688662082707296821112533351516773050343991015788576132619057588917857745748905303371752592099136703165151282333100494499323347128031948497690288176639447546152599173772000911565297841828485300937253530263374116722682295128167032344694730137174975142011502398045562092403230062956020616644587804005815099974069101832210673757163925038369891489885518417662205452242000145207860419586577722128862876236996653950204967238301154803919945512025034860200321202539316233694006359168439408091255927642403518104559241292762606479904975841448840597757301326350410559925209044618227232525672913734697817921967824675222388088469251797881683841017624251086627182469529353956562118710750276615251150565749892292784621212796020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Nearby Factorials

n	n!	Digits	Trailing Zeros
4091!	31672962...0000	13,002	1020
4092!	12960576...0000	13,006	1020
4093!	53047638...0000	13,009	1020
4094!	21717703...0000	13,013	1020
4095!	88933993...0000	13,016	1021
4096!	36427363...0000	13,020	1021
4097!	14924290...0000	13,024	1021
4098!	61159744...0000	13,027	1021
4099!	25069379...0000	13,031	1021
4100!	10278445...0000	13,035	1023
4101!	42151904...0000	13,038	1023

More factorial calculations

Here you can find answers to questions like: What is the number of zeros on the end of 4096 factorial What is the factorial of 4096? What is the last digits of factorial of 4096? How many trailing zeros in 4096 factorial? How many digits are there in 4096 factorial? Use the factorial calculator above to find the factorial of any natural between 0 and 10,000.

What is factorial?

Definition of factorial

The factorial is a quantity defined for any integer n greater than or equal to 0.

The factorial is the product of all integers less than or equal to n but greater than or equal to 1. The factorial value of 0 is, by definition, equal to 1. For negative integers, factorials are not defined. The factorial can be seen as the result of multiplying a sequence of descending natural numbers (such as 3 × 2 × 1).

The factorial symbol is the exclamation mark (!).

The factorial formula

If n is a natural number greater than or equal to 1, then

n! = n x (n - 1) x (n - 2) x (n - 3) ... 3 x 2 x 1

If n = 0, then n! = 1, by convention.

Example: 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

Shortcut to find trailing zeros in a factorial

Trailing zeros are a sequence of zeros in the decimal representation of a number, after which no other digits follow. This video shows how to find the trailing zeros of a factorial easily.

Table of factorials until 30

n	n!
1!	1	#
2!	2	#
3!	6	#
4!	24	#
5!	120	#
6!	720	#
7!	5040	#
8!	40320	#
9!	362880	#
10!	3628800	#
11!	39916800	#
12!	479001600	#
13!	6227020800	#
14!	87178291200	#
15!	1307674368000	#
16!	20922789888000	#
17!	355687428096000	#
18!	6402373705728000	#
19!	121645100408832000	#
20!	2432902008176640000	#
21!	51090942171709440000	#
22!	1124000727777607680000	#
23!	25852016738884976640000	#
24!	620448401733239439360000	#
25!	15511210043330985984000000	#
26!	403291461126605635584000000	#
27!	10888869450418352160768000000	#
28!	304888344611713860501504000000	#
29!	8841761993739701954543616000000	#
30!	265252859812191058636308480000000	#

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