Question

how many numbers between 100 and 200 are not divisible by any of the 2, 3 and 5 ď´ľincluding 100 and 200ď´ż?

Answer 1

We can solve it with the help of Euler formula.

2*3*5

= (1- 1/2)(1 - 1/3)(1 - 1/5)

= (1/2)(2/3)(4/5)

= 4/15

First we will look at the  numbers which are not Divisible between 1-1000

100 (4/15)

= 26

Now we will look at the  numbers which are not Divisible between 1-195

= 195 (4/15)

= 52

from 1-195  

52-26 = 26

And between the 196 - 200 there are only 2 numbers which are not divisible and those are 197 and 199

Total number = 26 + 2 = 28 is the answer.