Six has four factors and is in between the twin primes 5 and 7.
It's a multiple of 5, a multiple of 6 (since it's between twin primes), and less than 50. The only possibility is 30. To check: The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30
Since there are infinitely many primes, there are infinitely many numbers that are products of 3 primes.
Powers of primes
Assuming you are referring to the prime factors of the number, the product of the prime factors of any composite number is equal to the number itself.
No, twin primes are pairs of prime numbers that have only one number between them which is a composite number. For example, (3, 5) and (11, 13) are twin prime pairs with the composite number 4 and 12 respectively between them.
Factors are whole numbers that divide exactly into a whole number. These numbers have no remainder. Primes, on the other hand, have exactly two factors which are 1 and itself.
Any composite number will do. No primes!
Numbers with three factors are squares of primes: 4, 9, 25
Squares of primes.
It's a multiple of 5, a multiple of 6 (since it's between twin primes), and less than 50. The only possibility is 30. To check: The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30
105 and the primes are 3, 5, and 7
All numbers that are the square of primes have exactly 3 factors.
935
I'm not sure what you're asking. The smallest number that can't be between two primes is obviously 1. Once you start running into primes, every composite number is between at least two primes.
15 has more than exactly two factors (1, 3, 5, and 15), therefore it is composite. 17, 19, and 23 each have exactly 2 factors (1 and the number itself), so they are primes.
The squares of all primes have exactly 3 factors. The squares of primes under 40 are 4 (1, 2, and 4), 9 (1, 3, and 9), and 25 (1, 5, and 25).
Hi... Every integer can be expressed as the product of prime numbers (and these primes are it's factors). Since we can multiply any integer by 2 to create a larger integer which can also be expressed as the product of primes, and this number has more prime factors than the last, we can always get a bigger number with more prime factors. Therefore, there is no definable number with the most primes (much like there is no largest number)!