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Question about p prime in to n factorial!

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Question about p prime in to n factorial! [#permalink] New post 21 Jan 2011, 15:08
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So I was using the flash cards that Dreamy made for Quant, and had a question on the topic

Can you see if I am doing it right?

I made this up, it is not a real problem....

What is the highest power of 6 in 291! ?

by using quotient method this is how i worked:

291/6 = 48
48/6 = 8
8/6 = 1
2/6 =/ anything

48+8+1 = 57

Therefore, there are 57 powers of 6 in 291!?

Did I do this correctly?
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Re: Question about p prime in to n factorial! [#permalink] New post 21 Jan 2011, 16:01
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Wishbone wrote:
So I was using the flash cards that Dreamy made for Quant, and had a question on the topic

Can you see if I am doing it right?

I made this up, it is not a real problem....

What is the highest power of 6 in 291! ?

by using quotient method this is how i worked:

291/6 = 48
48/6 = 8
8/6 = 1
2/6 =/ anything

48+8+1 = 57

Therefore, there are 57 powers of 6 in 291!?

Did I do this correctly?


6 is not a prime number. When determining the highest power of non-prime in n! the approach should be slightly different.

Check this:
everything-about-factorials-on-the-gmat-85592.html (main thread about this issue with examples of determining the highest power of primes as well as non-primes in n!);

Other examples:
gmat-club-m12-100599.html
if-n-is-the-product-of-integers-from-1-to-20-inclusive-106289.html
facorial-ps-105746.html

As for your question: what is the highest power of 6 in 291!?

6=2*3 so you'll need as many 3-s as 2-s, so the power of 3 in 291! will determine the highest power of 6 in 291! (as highest power of 3 will be obviously less than the highest power of 2. Or in other words there will be more 3-s than 2-s in 291!, so the power of 3 will be limiting factor): 291/3+291/9+291/27+291/81+291/243=97+32+10+3+1=143 (the formula actually counts the number of factors 3 in 291!, but since there are at least as many factors 2, this is equivalent to the number of factors 6). So the highest power of 6 in 291! is 143.

P.S. I doubt that you'll be asked to determine the highest power of non-prime (except the power of 10) in n! on the GMAT.
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Re: Question about p prime in to n factorial! [#permalink] New post 21 Jan 2011, 17:12
as soon as i posted this i knew what i did wrong, that's why the example was power of 2 in 25!. must be prime. thanks for clearing that up
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Re: Question about p prime in to n factorial! [#permalink] New post 13 Jul 2014, 02:19
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Re: Question about p prime in to n factorial! [#permalink] New post 20 May 2015, 14:58
Hi,

So in the below, I don't follow why "3" will be the limiting factor? Also, if highest power of 3 will be less that that of 2 how does that mean more 3's than 2's in 291!? Maybe it is obvious but I am not able to figure this out.

"...so the power of 3 in 291! will determine the highest power of 6 in 291! (as highest power of 3 will be obviously less than the highest power of 2. Or in other words there will be more 3-s than 2-s in 291!..."

Thanks!
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Re: Question about p prime in to n factorial! [#permalink] New post 20 May 2015, 15:23
Ok never mind, it is because 3 is a larger number , it needs fewer powers to express a number!
Re: Question about p prime in to n factorial!   [#permalink] 20 May 2015, 15:23
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