Plz someone help me to solve this problem.

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Mathlover
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Plz someone help me to solve this problem.

Unread post by Mathlover » Sat Jun 11, 2011 1:31 pm

How many different positive integers divide 10! ?

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Mohaimin
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Re: Plz someone help me to solve this problem.

Unread post by Mohaimin » Sat Jun 11, 2011 5:13 pm

I am not giving the complete solution. Just telling one possible approach. Do the solution yourself or ask if you need more information.
First note that 10! has only the prime factors 2, 3, 5 and 7. The next prime 11 cannot be in 10! because it is bigger than 10.
Now you need to find out the maximum power of each of the primes that divides 10!.
So, you get the Prime Power Factorisation(PPF) of 10!
There is a way to find out number of factors from PPF.

Mathlover
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Re: Plz someone help me to solve this problem.

Unread post by Mathlover » Tue Jun 14, 2011 10:59 pm

the question was to find positive integers,not prime integers.

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Nadim Ul Abrar
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Re: Plz someone help me to solve this problem.

Unread post by Nadim Ul Abrar » Wed Jun 15, 2011 6:09 pm

You need to know the theorem that,
If n is any number such that
n=p^{a}p'^{b}........
Where p,p'.......
Then
the number of factors will be
(a+1)(b+1).....
And thats the number of divisor tooo;)
$\frac{1}{0}$

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Nadim Ul Abrar
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Re: Plz someone help me to solve this problem.

Unread post by Nadim Ul Abrar » Wed Jun 15, 2011 6:13 pm

The ans will be
270
$\frac{1}{0}$

Mathlover
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Re: Plz someone help me to solve this problem.

Unread post by Mathlover » Thu Jun 16, 2011 12:36 pm

thanks nadim......

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Nadim Ul Abrar
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Re: Plz someone help me to solve this problem.

Unread post by Nadim Ul Abrar » Thu Jun 16, 2011 5:38 pm

Thanks to u too . Cause u'r the first one thanked in this forum ;-)
$\frac{1}{0}$

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Tahmid Hasan
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Re: Plz someone help me to solve this problem.

Unread post by Tahmid Hasan » Thu Jun 16, 2011 10:28 pm

tao function is very helpful here i think.
বড় ভালবাসি তোমায়,মা

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Mohaimin
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Re: Plz someone help me to solve this problem.

Unread post by Mohaimin » Fri Jun 17, 2011 7:22 pm

Mathlover wrote:the question was to find positive integers,not prime integers.
I know, I did not give you the complete solution. Just gave some hints. I meant to solve it exactly how Nadim solved.
Nadim Ul Abrar wrote:You need to know the theorem that,
If n is any number such that
n=p^{a}p'^{b}........
Where p,p'.......
Then
the number of factors will be
(a+1)(b+1).....
And thats the number of divisor tooo;)
p, p`... should be prime. You did not mention that.

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Nadim Ul Abrar
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Location: B.A.R.D , kotbari , Comilla

Re: Plz someone help me to solve this problem.

Unread post by Nadim Ul Abrar » Sun Jul 10, 2011 3:56 pm

Sorry @ MOhaimin
$\frac{1}{0}$

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