# Thread: [SOLVED] SAT math page 657 #17

1. ## [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?

2. Hello,
Originally Posted by fabxx
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?

It's not that I don't want to help you, but you'll better understand and learn if you're not thouroughly given the answer. Also, have you tried anything ?

Hint : a prime number has only 2 factors : 1 and itself.

3. 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

4. Originally Posted by fabxx
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
Hmmm I wonder how you got them

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 ? )
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

5. mmm thanks for replying though (:

6. Originally Posted by fabxx
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
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}