What is the unit digit in the multiplication of 1× 3× 5× 7× 9× … × 999 ?

A natural number N is such that it can be expressed as N = p + q + r , where p, q and r are distinct factors of N. How many numbers below 50 have this property?

Three prime numbers p, q and r, each less than 20, are such that p - q = q - r . How many distinct possible values can we get for (p + q + r) ?

How many possible values of (p + q + r) are there satisfying (1)/(p) + (1)/(q) + (1)/(r) = 1 , where p, q and r are natural numbers (not necessarily distinct)?

A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?

Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30 What is the number of possible values of k?