## Question

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

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

## Answers

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#

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