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
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
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}