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December 1st, 2010, 01:09 PM   #1
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Please help with this math problem including primes

Let the letters p, q, and r represent different primes. Then p^2 qr^3 has 24 divisors. So would p^23. Use p, q, and r to describe all whole numbers having exactly the following number of divisors.

(a) 2
(b) 3
(c) 4
(d) 5
(e) 6
(f) 12
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December 1st, 2010, 03:26 PM   #2
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Re: Please help with this math problem including primes

(a)
(b)
(c)
(d)
(e)
(f) , , ,

In general, we get these by looking at all factorizations of the number, and using k-1 as an exponent for each factor k. For example, the factorizations of 12 are

12*1, 6*2, 4*3, and 3*2*2
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December 1st, 2010, 04:31 PM   #3
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Re: Please help with this math problem including primes

Hello, sophieT66!

Quote:


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[color=red]**[/color]


[color=beige]. . [/color]

















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December 2nd, 2010, 12:04 PM   #4
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Re: Please help with this math problem including primes

Good post Soroban, but one small correction:

pqr has 8 divisors, not 6.
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December 2nd, 2010, 04:41 PM   #5
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Re: Please help with this math problem including primes


Thanks for the heads-up, Dr.Steve !


Hello, Moderators:

We don't have an EDIT capability?

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December 2nd, 2010, 04:55 PM   #6
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Re: Please help with this math problem including primes

The editing of posts was recently increased from 1 hour to 12 hours after the post is made.

I'm sure [color=#BF0000]julien[/color] has a good reason for imposing a time limit on post editing.

I edited your post.
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