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16 November, 02:02

If x is a positive integer, how many positive integers less than x are divisors of x? x2 is divisible by exactly 4 positive integers less than x2. 2x is divisible by exactly 3 positive integers less than 2x.

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  1. 16 November, 05:25
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    "x ^ 2 is divisible by exactly 4 positive integers less than x ^ 2"

    Step-by-step explanation:

    Let's review each statement:

    "x ^ 2 is divisible by exactly 4 positive integers less than x ^ 2"

    This means that:

    x ^ 2 = a ^ 4,

    Where a is a prime number.

    The reason is that the number of factors of a ^ 4 = 4. For example, say a ^ 4 = 2 ^ 4 = 16. The no. of the factors of 16 are 1, 2, 4 and 8. 16 is not counted because they mention everything less than x ^ 2, that is, everything except ^ 4 and 2 ^ 4 is 16, therefore it is not included.

    So we already know that the first statement is fine, therefore it is the correct answer.
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