Question

How many positive integers between 1 and 2101 is divisible by a prime number?

Answer 1

See a solution process below:

Explanation:

By definition of a positive integer, every positive integer is divisible by `2`. Therefore, every positive integer less than 2101 is divisible by at least one prime number in the the set.

The formula for finding the number of even integers between `2` and some positive integer greater than `2` is:

`(n - 2)/2 + 1`

Substituting 2100 for `n` and evaluating the expression gives:

`(2100 - 2)/2 + 1 = 2098/2 + 1 = 1049 + 1 = 1050`