Question

A number is called squarefree if it is not divisible by the square of a positive integer greater than one. find the number of square free positive integers less than 100.

Answer 1

Count the number of positive integers less than 100 that do not contain any perfect square factors greater than 1.

Possible perfect squares are the squares of integers 2-9.
In fact, only squares of primes need be considered, since for example, 6^2=36 actually contains factors 2^2 and 3^2.
Tabulate the number (in [ ])of integers containing factors of 
2^2=4: 4,8,12,16,...96 [24]
3^2=9: 9,18,....99  [11] 
5^2=25: 25,50,75  [3]
7^2=49:  49,98 [2]

So the total number of integers from 1 to 99
N=24+11+3+2=40
=>
Number of positive square-free integers below 100 = 99-40 = 59