How many integers between 100 and 150, inclusive, cannot be
evenly divided by 3 nor 5?
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Answer Posted / ramabramham
Number of integers that divide 3:
the range is 100-150
Relevant to this case, we take 102 - 150 (since 102 is the
first to div 3)
102 = 34*3
150= 50*3, so we have 50-34+1 = 17 multiples of 3
For multiples of 5,
100=5*20
150=5*30
30-20+1 =11
Now we have a total of 27 integers, but we double counted
the ones that divide BOTH 3 AND 5, ie 15.
105 is the first to divide 15.
105=15*7
150=15*10
10-7+1 = 4 integers
So our total is 17+11-4 = 24 integers that can be divided
by either 3 or 5 or both.
51 integers - 24 integers = 27 that cannot be evenly divided
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