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Everything about Factorials on the GMAT

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Re: Everything about Factorials on the GMAT [#permalink] New post 17 Apr 2014, 02:09
Bunuel wrote:
agavaqif wrote:
Very nice post, indeed.is there anything about factors of factorial?


Check the links in my signature below.

Thankss. Actually after writing this post I found necessery info from links in your profile. Thanks again
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Re: Everything about Factorials on the GMAT [#permalink] New post 11 Jun 2014, 12:18
How many zeros are in the end (after which no other digits follow) of 32!?

\frac{32}{5}+\frac{32}{5^2}=6+1=7. Notice that the denominators must be less than or equal to 32 also notice that we take into account only the quotient of division (that is \frac{32}{5}=6 not 6.4). Therefore, 32! has 7 trailing zeros.

The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero.
how come we divide 32 by 5?
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Re: Everything about Factorials on the GMAT [#permalink] New post 11 Jun 2014, 13:13
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sagnik2422 wrote:
How many zeros are in the end (after which no other digits follow) of 32!?

\frac{32}{5}+\frac{32}{5^2}=6+1=7. Notice that the denominators must be less than or equal to 32 also notice that we take into account only the quotient of division (that is \frac{32}{5}=6 not 6.4). Therefore, 32! has 7 trailing zeros.

The formula actually counts the number of factors 5 in n!, but since there are at least as many factors 2, this is equivalent to the number of factors 10, each of which gives one more trailing zero.
how come we divide 32 by 5?


Well, this is done according to the formula given there.
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Re: Everything about Factorials on the GMAT [#permalink] New post 27 Aug 2014, 05:05
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I don't know the proof but I thought this would be useful:

Where a and b are integers,

(a + b)! is divisible by a!.b!
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Re: Everything about Factorials on the GMAT [#permalink] New post 12 Dec 2014, 18:57
Really valuable, thanks!
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Re: Everything about Factorials on the GMAT [#permalink] New post 22 Apr 2015, 00:07
A more generalised method for finding powers of non prime numbers in a factorial:

Assuming we have to find the power of 12 in 30!

Now, 30 = 2 * 3 * 5.

Find what the highest power of each prime is in the given factorial (by the same method as given by Bunuel)

We have 25 + 12 + 6 + 3 + 1 = 47 2s in 50!

16 + 5 + 1 = 22 3s in 50!

10 + 2 = 12 5s in 50!

We need a combination of one 2, one 3 and one 5 to get 30. In the given factorial we have only 12 5s. Hence only twelve 30s are possible. So the greatest power of 30 in 50! is 12.

Similarly we can find powers of 4 (number of pairs of 2) etc.

Hope it helps.
Re: Everything about Factorials on the GMAT   [#permalink] 22 Apr 2015, 00:07

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