math

If p,r, and s are three different prime numbers greater than 2 and n = p*r*s, how many positive factors, including 1 and n, does n have?

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  1. 8

    here are two ways to look at it,

    1. how many subsets can you form with 3 elements, including the null set (the factor 1), and the set of all elements (the n) -----> 2^3 = 8

    or

    2. we can use the p in 2 ways, that is, we can either include it or we can not include it, so 2 x ...
    we can use the r in 2 ways, that is, we can either include it or we can not include it, so 2 x 2 x ..
    we can use the s in 2 ways, that is, we can either include it or we can not include it, so 2 x 2 x 2

    2 x 2 x 2 = 8,
    this would include not taking any, which might correspond to the factor 1, and includes taking all 3 of them, which corresponds to n.

    try it with the 3 numbers 3,5 and 7

    factors would be
    1
    2
    5
    7
    3*5
    3*7
    5*7 and finally
    3*5*7, count them, there are 8

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