Question

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.

Answer 1

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

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.