Question

how many numbers less than 500 are there with exactly 3 factor​

Answer 1

Answer:

The question is too vague to answer. If you mean “how many numbers have exactly three prime factors, each less than 100,” then we could calculate the answer by counting the number of primes less than 100 (25 of them), and then calculate the number of combinations of three of them: (25*24*23) = 13,800 such numbers.

Edit: Ah, you changed the question to be clearer! “Numbers that have exactly three factors” is still not perfectly clear, but I think you mean *all* factors other than 1. If so, there are two classes of numbers that meet this criterion: (1) products of two primes; and (2) cubes of primes. Products of two primes, p, and q, have factors p, q, and p*q. Cubes of primes p have factors p, p^2, and p^3. Here’s an enumeration of these numbers under 100:

6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 74, 82, 86, 94,

15, 21, 33, 39, 51, 57, 69, 87, 93,

35, 55, 65, 85, 95,

77, 91,

8, 27

So that is 32 such numbers.

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