2nd part of this question ….
Determine the number of positive integer(<=720)
which are not divisible by any of 2,3, or 5.
solution:
total number of positive integers (<=720)=720
no. of integers divisible by 2=floor(720/2)=360
no. of integers divisible by 3=floor(720/3)=240
no. of integers divisible by 5=floor(720/5)=144
Here we are going to see the formula for (A U B U C).
n(AUBUC)=n(A)+n(B)+n(C)-n(AnB)-n(BnC)-n(CnA)+n(AnBnC)
so number of positive integers(<720) which are divisible by any of 2,3,or 5:
=floor(720/2)+floor(720/3)+floor(720/5) – floor(720/6) – floor(720/15) – floor(720/10).+floor(720/30)
= 360+240+144 -120 -48-72+24
= 528 positive integers numbers are there which are divisible by 2 ,3 or 5. between 1 to 720.
SO answer will be 720-528=192 numbers which are not divisible by 2 ,3 or 5.
