If P, R, and S are three different prime numbers greater than 2 and N=P x R x S (x is multiply), how many positive factors including 1 and N, does N have?

Thanks in advance

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- Sep 28th 2008, 01:36 AMfabxx[SOLVED] SAT math page 657 #17
If P, R, and S are three different prime numbers greater than 2 and N=P x R x S (x is multiply), how many positive factors including 1 and N, does N have?

Thanks in advance - Sep 28th 2008, 01:39 AMMoo
- Sep 28th 2008, 01:49 AMfabxx
I tried substituting numbers. Once i got 3 and another time i got 0. For example i substituted 3, 7, 11 as p, s, r and i got 0 for positive factors of n. And then i substituted 3, 5,7 as p, s, r and I got 3. Is there any other way? Thanks in advance

- Sep 28th 2008, 02:09 AMMoo
Hmmm I wonder how you got them (Surprised)

And I wonder how I'll explain it to you...

1 is a factor

P, R, S are obviously factors

N is a factor.

That makes 5.

P x R is obviously a factor, and so are P x Q and Q x R.

That makes 8.

Actually, these are all the possibilities. Why ? Note that any number can be written as a product containing at least one prime. Let d be a prime divisor of a number that would divide N (are you still here ? (Doh))

If d divides N, then it divides either P, R, S. But the only numbers dividing P,R or S are themselves or 1.

So d has to be one of the listed possibilities above...

I'm really sorry if it is not clear, I'm trying my best to explain it :( - Sep 28th 2008, 02:49 AMfabxx
mmm thanks for replying though (:

- Sep 28th 2008, 07:09 AMshailen.sobhee
Deliberate on remember this line from Moo:

**Note that any number can be written as a product containing at least one prime.**

Let's come to your problem. If its SATs, AS A RULE, never take small test values, like -1,0,1,2,3. That's just an advice to apply to other questions, not specifically here.

For this number, just take 3 different prime numbers, and list all their factors.

Lets take 5,7 and 11.

$\displaystyle 5*7*11=385$

Factors of $\displaystyle 385$ are:

$\displaystyle 1 , 385$

$\displaystyle 5 , 77$

$\displaystyle 7 , 55$

$\displaystyle 11 , 35$

Count them and the answer is $\displaystyle 8$ (the question says including 1 and n)

Btw, Latex is cool. However, typing formulas would be easier if the tool underlying the conversions could interpret mathematical operations automatically. For instance, 1/n could be directly converted to $\displaystyle

\frac{1}{n}$, without the 'verbose' \frac{1}{n}