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How many primes less than 1000 are divisible by 7?
Just 7. Any other number divisible by 7 isn't prime.
Find smallest positive divisor of an integers other then 1?
There is no such number. If you restrict yourself to integers, there are numbers - such as primes, that are not divisible by an integer other than one. And if you do not restrict yourself to intgers, then there is no smallest number sincce given any number, half that number will be smaller and will be a divisor.
The largest integer that is not the product of two or more different primes?
The largest integer that is not the product of two or more different primes would be the largest prime number. Because there are an infinite number of prime numbers, there is no largest integer that is not the product of two or more different primes.
Are there more primes or composites?
In any large range of numbers, more so the higher and larger the range is, there will be more composites than primes. It is far more likely that a given number will be divisible by some number less than the number itself, the higher you go.
If told that 'q' 'p' and 'r' are distinct primes and that there exists 'n' such that 'n equals p x q x r' How many positive factors of 'n' are there and How do you determine what they are?
If p, q and r are distinct primes and n=pxqxr then n will have 8 factors, all of which will be positive since prime numbers are all positive, which are: n(pqr), pq, pr, qr, p, q, r and 1. Here there were 3 distinct primes so the number of positive factors is 2^3. In general if you had p distinct primes then you would have 2^p positive factors.
