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

1 Answer
Oct 1, 2017

Answer:

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#