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Among the numbers 1, 2, 3, ..., 1000, how many numbers are multiples of 5 or multiples of 7?

 May 14, 2020
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Number  of integers divisible  by  5  from 1 to 1000 =  1000 / 5  = 200

 

Number of integers  divisible by 7  from 1 to 1000 =   integer part (1000/7)  =   142

 

But we  must subtract out  those integers  which are multiples of 5 and 7, ie., all the  multiples of 35

 

So   integer part (1000/35)  =  28

 

So  ....number of integers that are multiples of 5 or 7  =  200 + 142  - 28  =   314

 

 

cool cool cool

 May 14, 2020

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