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of-the-integers-101-to-400-including-101-and-400-themselves-how-many-are-not-divisible-by-3-or-5-

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Question Number 154301 by joki last updated on 16/Sep/21
of the integers 101 to 400 (including 101 and 400 themselves) how many are not divisible by 3 or 5?
oftheintegers101to400(including101and400themselves)howmanyarenotdivisibleby3or5?
Answered by mr W last updated on 16/Sep/21
400−100=300 numbers divisible by 3: ⌊((400)/3)⌋−⌊((100)/3)⌋=100 divisible by 5: ⌊((400)/5)⌋−⌊((100)/5)⌋=60 divisible by 15: ⌊((400)/(15))⌋−⌊((100)/(15))⌋=20 ⇒300−100−60+20=160
400−100=300numbersdivisibleby3:⌊4003⌋−⌊1003⌋=100divisibleby5:⌊4005⌋−⌊1005⌋=60divisibleby15:⌊40015⌋−⌊10015⌋=20⇒300−100−60+20=160

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