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Math Help - [SOLVED] SAT math page 657 #17

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    [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
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    Moo
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    Hello,
    Quote Originally Posted by fabxx View Post
    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
    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.
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    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
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    Moo
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    Quote Originally Posted by fabxx View Post
    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
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    mmm thanks for replying though (:
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    Quote Originally Posted by fabxx View Post
    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.

    5*7*11=385

    Factors of 385 are:
    1 , 385
    5 , 77
    7 , 55
    11 , 35

    Count them and the answer is 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 <br />
\frac{1}{n}, without the 'verbose' \frac{1}{n}
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