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

Oct 1, 2017

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:

$\frac{n - 2}{2} + 1$

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

$\frac{2100 - 2}{2} + 1 = \frac{2098}{2} + 1 = 1049 + 1 = 1050$