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.

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