How many whole numbers between 1 and 150 have exactly 3 different factors?

Answer 1

3

Answer 2

There are five whole numbers between 1 and 150 that have exactly 3 different factors. Whole numbers between 1 and 150 with exactly 3 different factors must be the square numbers whose square roots are prime.
To find the complete list begin counting... skip 1, not prime; 2 is prime and 2 squared is 4; 3 is prime and 3 squared is 9; skip 4 b/c it is not prime; 5 is prime and 5 squared is 25; 6 not prime; 7 prime and 7 squared is 49; 8 not prime; 10 not prime; 11 prime and squared is 121; 12 is not prime; 13 prime, but squared it is greater than 150. The complete list is 4, 9, 25, 49, and 121. 4 has 1, 2, 4 9 has 1, 3, 9 25 has 1, 5, 25 49 has 1, 7, 49 121 has 1, 11, 121

Answer 3

Whole numbers with exactly 3 different factors are square numbers. To have exactly 3 factors, the number must be a perfect square of a Prime number, as the factors would be 1, the prime number itself, and the square root of the number. The prime numbers less than the square root of 150 are 2, 3, 5, 7, 11, and 13. The perfect squares of these primes that are less than or equal to 150 are 4, 9, 25, and 49. So, there are 4 whole numbers between 1 and 150 that have exactly 3 different factors.