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If p is the product of the integers

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by Tryingmybest » Wed Mar 25, 2009 10:12 am
IMO E

P = 1*2*3*..*30

Let us take the highest integer in choice which is 18

K= 18

We need to check if 3K is a factor of P

P/3K = (1 * 2 * 3 * ... * 30) /( 3 * 18 )
which will be an integer

So E

Please correct me if I am wrong
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by lilu » Wed Mar 25, 2009 10:27 am
Something tells me that it should be 3^K instead of 3*k...
Please let me know if that is the case, then I'll explain how the shortcut (Ian's explanations in one of the post from a couple of weeks ago) works with the highest powers possible.
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by krisraam » Wed Mar 25, 2009 6:34 pm
If its 3^K . The answer will be 14.

BTW whats the shortcut?


Thanks
Raama
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by eldar » Fri Mar 27, 2009 1:46 pm
Hi guys, here is my reasoning:

If in the expression 1*2*3*4*5..*29*30

We find that all the factors integer that are multiple of 3 are

3,6=3*2,9=3*3,12=3*4,15=3*5,18=3*3*2,21=7*3,24=8*3,27=3*3*3,30=10*3

So the maximum is 3^14
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by sureshbala » Fri Mar 27, 2009 9:53 pm
In order to calculate the highest power of a prime number in any factorial here is a quick way.....

Let us consider the question itself.....

We have to calculate the highest power of 3 in 30!

The procedure is simple. Go for the successive division.

30/3 = 10

10/3 = 3 (Go for the quotient and don't worry about the remainder)

3/3 = 1

Now add these results i.e. 10+3+1 = 14.

Hence the highest power of 3 in 30! = 14.
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Let us look at one more example

Highest power of 7 in 120!

120/7 = 17

17/7 = 2

Hence the highest power of 7 in 120! = 17+2=19

Sometime later I will let you know the logic behind this calculation and also how to calculate highest power of any number in any given product (not only factorial)

Hope this helps
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hi

by srivas » Sat Mar 28, 2009 8:47 am
lilu wrote:Something tells me that it should be 3^K instead of 3*k...
Please let me know if that is the case, then I'll explain how the shortcut (Ian's explanations in one of the post from a couple of weeks ago) works with the highest powers possible.
yes it is 3^k
Gmat710,, Hyd
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