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Question Number 154301 by joki last updated on 16/Sep/21

$$\mathrm{of}\mathrm{the}\mathrm{integers}101\mathrm{to}400(\mathrm{including}101\mathrm{and}400$$$$\mathrm{themselves})\mathrm{how}\mathrm{many}\mathrm{are}\mathrm{not}\mathrm{divisible}\mathrm{by}3\mathrm{or}5?$$

Answered by mr W last updated on 16/Sep/21

$$400-100=300numbers$$$$divisibleby3:\lfloor \frac{400}{3}\rfloor -\lfloor \frac{100}{3}\rfloor =100$$$$divisibleby5:\lfloor \frac{400}{5}\rfloor -\lfloor \frac{100}{5}\rfloor =60$$$$divisibleby15:\lfloor \frac{400}{15}\rfloor -\lfloor \frac{100}{15}\rfloor =20$$$$\Rightarrow 300-100-60+20=160$$

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