The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is
Explanation:
Positive integers having exactly two distinct factors other than 1 and itself will be of the form a × b or a3, where a and b are prime numbers.
Case 1: a × b < 50. Possible combinations are: If one of them is 2, the other prime number can be 3, 5, 7, 11, 13, 17, 19, 23 i.e., 8 possibilities. If one of them is 3, the other prime number can be 5, 7, 11, 13 i.e., 4 possibilities. If one of them is 5, the other prime number can be 7 i.e., 1 possibility. ∴ 13 cases.
Case 2: a3. Possible values of a are 2 and 3 i.e., numbers are 8 and 27. ∴ 2 cases.
∴ Total 13 + 2 = 15 such numbers are possible.
Hence, 15.
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