720!
The value of 720! is a large number.
Just how many digits does it have?
How many of the digits are 0?
How many of the other digits from 1 to 9?
I guess this is to hard.
Here's a link that will make it easy.
http://www.numberempire.com/factorialcalculator.php
Just how many digits does it have?
How many of the digits are 0?
How many of the other digits from 1 to 9?
I guess this is to hard.
Here's a link that will make it easy.
http://www.numberempire.com/factorialcalculator.php
Labels: mathschallenge
posted by Ragknot at
12:06 PM
8 Comments:
there r 178 zeros i think.
The others i may calculate later, gtg
To gtg:
That's a good start.
"720!" does end with 178 zeros.
It is interesting how large factorials end with a huge number of zeros. I once figured out why, but that is another question for ToM.
few thungs to clear:
1)My name is NOT gtg, i was just saying, ill do the rest of the questions later, i got to go!! :P
2)I dont noe how to get the other digits, ill try.
well,
0 - 178 times
this was easy i just used this:
[720/5]+[720/25]+[720/125]+
[720/6250]+....till the answer comes 0
NOTE: [] denote that only the integer part of the answer is to be taken, i.e 9.9=9, 5.100=5.999=5
as 0 has to come from 10, i.e. 2*5 it is obvious tht 2 and five r needed to make each 0 and so i found no. on 0s tht way
the other questions pose a problem to me still trying t work on it, i just thought id post my explanation, if someone have a better way of doing it plz tell.
well, i got 2 ways to get the other 2 answers,:
but both need calculators.
1) I was soo irritated, that i just did it on my scientific calculator!!
2) as i wasnt satisfied with tht, i used stirlings approximation with log. and got the answer as 1747 numbers totally.
So, the 1)total number of digits is 1747, 2)zeros are 178,
and finally 3) 1569 other digits from 1-9
PS: for those who dont noe sterlings approximation, it is:
n! = (2.pi.n)^1/2 (n/e)^n
wikipedia has the whole explanation and derivation on it.
The last 178 digits are zero, but that's not all the zeros. That might be close to 1/2 of the zeros.
The number of digits is 1747.
That means that 1569 digits are not part of the trailing zeros. Those are almost evenly distributed between 0 and 9.
The first 100 digits are...
2601218943565795100204903227081043611191521875016945785727541837850835631156947382240678577958130457
260121894356579510020490322708104361119152187501694578572754
183785083563115694738224067857795813045708261992057589224725
953664156516205201587379198458774083252910524469038881188412
376434119195104550534665861624327194019711390984553672727853
709934562985558671936977407000370043078375899742067678401696
720784628062922903210716166986726054898844551425719398549944
893959449606404513236214026598619307324936977047760606768067
017649166940303481996188145562519559256691883082551494294759
653727484562462882423452659778973774089646655399243592878621
251596748322097602950569669992728467056374713753301924831358
707612541268341586012944756601145542074958995256354306828863
463108496565068277155299625679084523570255218622235813001670
083452344323682193579318470195651072978180435417389056072742
804858399591972902172661229129842051606757903623233769945396
419147517556755769539223380305682530859997744167578435281591
346134039460490126954202883834710136373382448450666009334848
444071193129253769465735433737572477223018153403264717753198
453734147867432704845798378661870325740593892421570969599463
055752106320326349320922073832092335630992326750440170176057
202601082928804233560664308988871029738079757801305604957634
283868305719066220529117482251053669775660302957404338798347
151855260280533386635713910104633641976909739743228599421983
704697910995630338960467588986579571117656667003915674815311
594398004362539939973120306649060132531130471902889849185620
376666916446879112524919375442584589500031156168297430464114
253807489728172337595538066171980140467793561479363526626568
333950976000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000000000000000000000000000000000
0000000
Answer:
1747 digits with the following distribution.
0- 332
1- 142
2- 148
3- 164
4- 152
5- 172
6- 169
7- 161
8- 138
9- 169
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